editing

approved

The initial terms are {1, 1373}, {2, 1319}, {3, 1033}, {4, 1493}, {5, 853}, {6, 839}, {7, 593}, {8, 1093}, {9, 461}, {10, 487}, . . . , {73, 11597}, {74, 12263}, {75, 12697}, {76, 13877}, {77, 13381}, {78, 14087}, {79, 14561}, {80, 15541}, {81, 15791}, {82, 16553}

Clearified Clarified the definition of the sequence and added a PARI program. _Harry J. Smith, _, with help from Maximilian _M. F. Hasler, _, Jan 31 2009

approved

editing

_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Jun 09 2008

The polynomials are tested in a cycle beginning with t[1 + mod [x,4]], i.e. when x==0 mod 4, they are tested in order t1,t2,t3,t4; when x==1 mod 4, they are tested in the order t2,t3,t4,t1, etc. If none of the polynomials are prime, no value is given. [From _Harry J. Smith (hjsmithh(AT)sbcglobal.net), _, Jan 28 2009, Jan 31 2009]

Harry J. Smith, <a href="/A139414/a139414.txt">Comments on this sequence</a>

nonn,new

nonn

a(Xx) = if one of {4x^2 - 146x + 1373, 4x^2 - 144x + 1459, 4x^2 - 142x + 1301, 4x^2 - 140x + 1877} is prime, then pick that prime in sequence.

What is more than one is prime? What if The polynomials are tested in a cycle beginning with t[1 + mod [x,4]], i.e. when x==0 mod 4, they are tested in order t1,t2,t3,t4; when x==1 mod 4, they are tested in the order t2,t3,t4,t1, etc. If none of the four is polynomials are prime? - njas, Jun 09 2008, no value is given. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jan 28 2009, Jan 31 2009]

Harry J. Smith, <a href="a139414.txt">Comments on this sequence</a>

The initial terms are: {1, 1373}, {2, 1319}, {3, 1033}, {4, 1493}, {5, 853}, {6, 839}, {7, 593}, {8, 1093}, {9, 461}, {10, 487}, . . . {73, 11597}, {74, 12263}, {75, 12697}, {76, 13877}, {77, 13381}, {78, 14087}, {79, 14561}, {80, 15541}, {81, 15791}, {82, 16553}

{0, 1373}, {1, 1319}, {2, 1033}, {3, 1493}, {4, 853}, {5, 839}, {6, 593}, {7,

1093}, {8, 461}, {9, 487}, {10, 281}, {11, 821}, {12, 197}, {13, 263}, {14,

97}, {15, 677}, {16, 61}, {17, 167}, {18, 41}, {19, 661}, {20, 53}, {21,

199}, {22, 113}, {23, 773}, {24, 173}, {25, 359}, {26, 313}, {27, 1013}, {28,

421}, {29, 647}, {30, 641}, {31, 1381}, {32, 797}, {33, 1063}, {34, 1097},

{35, 1877}, {36, 1301}, {37, 1607}, {38, 2333}, {39, 1847}, {40, 1933}, {41,

2203}, {42, 2393}, {43, 3253}, {44, 2693}, {45, 3079}, {46, 3121}, {47,

4133}, {48, 3581}, {49, 4007}, {50, 4201}, {51, 4519}, {52, 4597}, {53,

5011}, {54, 5297}, {55, 6277}, {56, 5741}, {57, 6247}, {58, 6521}, {59,

7541}, {60, 7013}, {61, 7559}, {62, 7873}, {63, 8933}, {64, 8627}, {65,

8999}, {66, 10061}, {67, 10453}, {68, 9941}, {69, 10567}, {70, 11677}, {71,

12101}, {72, 11597}, {73, 12263}, {74, 12697}, {75, 13877}, {76, 13381}, {77,

14087}, {78, 14561},

a = {4x^2 - 146x + 1373, 4x^2 - 144x + 1459, 4x^2 - 142x + 1301, 4x^2 - 140x + 1877}; (* functional "if" ladder to switch polynomials*) g[x_] := If[PrimeQ[a[[1 + Mod[x, 4]]]], a[[1 + Mod[x, 4]]], If[PrimeQ[a[[1 + Mod[x + 1, 4]]]], a[[1 + Mod[x + 1, 4]]], If[PrimeQ[a[[1 + Mod[x + 2, 4]]]], a[[1 + Mod[x + 2, 4]]], If[PrimeQ[a[[1 + Mod[x + 3, 4]]]], a[[1 + Mod[x + 3, 4]]], a[[1 + Mod[x, 4]]]]]]]; Flatten[Table[If[PrimeQ[g[x]], g[x], {}], {x, 0, 500}]] Length[%] Sort[Table[If[PrimeQ[g[x]], {x, g[x]}, {}], {x, 0, 500 }]];

(PARI) {n=0; for( x=0, 12022, t=[4*x^2-146*x+1373, 4*x^2-144*x+1459, 4*x^2-142*x+1301, 4*x^2-140*x+1877]; for(i=0, 3, if( isprime( p=t[ (x+i)%4+1 ]), print(n++, " "p); write("b139414.txt", n, " "p); break)))}

Cf. A155814.

nonn,obsc,new

Edited by njas, Jun 09 2008Clearified the definition of the sequence and added a PARI program. Harry J. Smith, with help from Maximilian Hasler, Jan 31 2009

a(X) = if one of {4x^2 - 146x + 1373, 4x^2 - 144x + 1459, 4x^2 - 142x + 1301, 4x^2 - 140x + 1877} is prime, then pick that prime in sequence.

1373, 1319, 1033, 1493, 853, 839, 593, 1093, 461, 487, 281, 821, 197, 263, 97, 677, 61, 167, 41, 661, 53, 199, 113, 773, 173, 359, 313, 1013, 421, 647, 641, 1381, 797, 1063, 1097, 1877, 1301, 1607, 2333, 1847, 1933, 2203, 2393, 3253, 2693, 3079, 3121, 4133

1,1

What is more than one is prime? What if none of the four is prime? - njas, Jun 09 2008

Based on correspondence with Aldrich Stevens.

The initial terms are:

{0, 1373}, {1, 1319}, {2, 1033}, {3, 1493}, {4, 853}, {5, 839}, {6, 593}, {7,

1093}, {8, 461}, {9, 487}, {10, 281}, {11, 821}, {12, 197}, {13, 263}, {14,

97}, {15, 677}, {16, 61}, {17, 167}, {18, 41}, {19, 661}, {20, 53}, {21,

199}, {22, 113}, {23, 773}, {24, 173}, {25, 359}, {26, 313}, {27, 1013}, {28,

421}, {29, 647}, {30, 641}, {31, 1381}, {32, 797}, {33, 1063}, {34, 1097},

{35, 1877}, {36, 1301}, {37, 1607}, {38, 2333}, {39, 1847}, {40, 1933}, {41,

2203}, {42, 2393}, {43, 3253}, {44, 2693}, {45, 3079}, {46, 3121}, {47,

4133}, {48, 3581}, {49, 4007}, {50, 4201}, {51, 4519}, {52, 4597}, {53,

5011}, {54, 5297}, {55, 6277}, {56, 5741}, {57, 6247}, {58, 6521}, {59,

7541}, {60, 7013}, {61, 7559}, {62, 7873}, {63, 8933}, {64, 8627}, {65,

8999}, {66, 10061}, {67, 10453}, {68, 9941}, {69, 10567}, {70, 11677}, {71,

12101}, {72, 11597}, {73, 12263}, {74, 12697}, {75, 13877}, {76, 13381}, {77,

14087}, {78, 14561},

a = {4x^2 - 146x + 1373, 4x^2 - 144x + 1459, 4x^2 - 142x + 1301, 4x^2 - 140x + 1877}; (* functional "if" ladder to switch polynomials*) g[x_] := If[PrimeQ[a[[1 + Mod[x, 4]]]], a[[1 + Mod[x, 4]]], If[PrimeQ[a[[1 + Mod[x + 1, 4]]]], a[[1 + Mod[x + 1, 4]]], If[PrimeQ[a[[1 + Mod[x + 2, 4]]]], a[[1 + Mod[x + 2, 4]]], If[PrimeQ[a[[1 + Mod[x + 3, 4]]]], a[[1 + Mod[x + 3, 4]]], a[[1 + Mod[x, 4]]]]]]]; Flatten[Table[If[PrimeQ[g[x]], g[x], {}], {x, 0, 500}]] Length[%] Sort[Table[If[PrimeQ[g[x]], {x, g[x]}, {}], {x, 0, 500}]];

nonn,obsc,new

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 09 2008

Edited by njas, Jun 09 2008

approved