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A081640
a(n) = n-th prime of class 12- according to the Erdős-Selfridge classification.
5
14920303, 18224639, 24867247, 26532953, 34548443, 38003011, 39800743, 41319599, 41443483, 45604771, 46432667, 47247763, 49734341, 49734493, 49749439, 51591833, 53014667, 55257977, 59681383, 59700749, 60804817
OFFSET
1,1
COMMENTS
The first 184 resp. 300 terms of A081430 allow us to deduce 44 resp. 84 consecutive terms of this sequence. - M. F. Hasler, Apr 05 2007
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, A18.
LINKS
FORMULA
{ a(n) } = { p = 2*m*A081430(k)+1 | k=1,2,...,oo and m=1,2,... such that p is prime and m has no factor of class > 11- } - M. F. Hasler, Apr 05 2007
EXAMPLE
a(1) = 14920303 = 1+2*A081430(3)*3 is the smallest 12- prime
MATHEMATICA
PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] - 1]]; ClassMinusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[3610000], ClassMinusNbr[ Prime[ # ]] == 12 &]]
PROG
(PARI) nextclassminus( a, p=1, n=[] )={ while( p, n=concat(n, p); p=0; for( i=1, #a, if( p & 2*a[i] >= p-1, break); for( k=ceil(n[ #n]/2/a[i]), a[ #a]/a[i], if( p & 2*k*a[i] >= p-1, break); if( isprime(2*k*a[i]+1), p=2*k*a[i]+1; break(1+(k==1)); )))); vecextract(n, "^1")}; A081640 = nextclassminus(A081430) \\ M. F. Hasler, Apr 05 2007
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Mar 23 2003
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 21 2007
STATUS
approved