A100370 - OEIS

A100370

Primes in A099756, sorted.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 59, 61, 67, 79, 83, 89, 101, 103, 107, 109, 127, 137, 139, 149, 151, 157, 163, 167, 179, 181, 211, 227, 239, 241, 251, 257, 263, 269, 281, 283, 307, 347, 349, 359, 367, 379, 389, 401, 409, 431, 449, 457, 461

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Inspired by A099756.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..950

EXAMPLE

Positions of "minimal terms" (see A007809) inside A099756 and here, in A100370, are {2,8,31,138,320,574,779,900,942,950} or {1,6,23,84,250,494,721,873,934,950} respectively.

This is because the orders of A099756 and A100370 are based on different criteria.

MATHEMATICA

<<DiscreteMath`Combinatorica` tm=TimeUsed[]; ta={{0}}; upps=PrimePi[{11, 787, 22259, 70879, 607889, 4456789, 40456789, 304456879, 1123465789, 10123457689}]; Do[ks1=KSubsets[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, hu]; Table[fla=1; Do[If[Equal[Union[IntegerDigits[Prime[n]]], Part[ks1, j]]&&Equal[fla, 1], ta=Append[ta, Prime[n]]; Print[Prime[n]]; fla=0], {n, PrimePi[1+10^(hu-1)], Part[upps, hu]}], {j, 1, Length[ks1]}], {hu, 1, 10}]; {ta=Union[Delete[ta, 1]], TimeUsed[]-tm} (* program displays hits and measures CPU-time too *)

ss = Subsets[ Range[0, 9], 10]; dlt = {1, 2, 6, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 30, 31, 32, 34, 38, 41, 42, 43, 45, 47, 49, 52, 53, 66, 67, 68, 70, 74, 77, 78, 79, 81, 83, 85, 88, 89, 127, 128, 130, 132, 134, 137, 153, 157, 159, 162, 168, 211, 212, 214, 216, 218, 221, 237, 241, 243, 246, 252, 332, 334, 337, 343, 373, 458, 460, 463, 469, 499, 604, 730}; ss = Delete[ss, {#} & /@ dlt]; k = 1; lst = {}; f[n_] := Block[{id = ss[[n]], p = NextPrime[ NestWhileList[ Quotient[#, 10] &, FromDigits[ ss[[n]]], # > 0 &][[-2]]*10^(Length[ss[[n]]] - If[ Mod[ FromDigits@ ss[[n]], 3] == 0, 0, 1]) - 1]}, While[ Union@ IntegerDigits@ p != id, p = NextPrime@ p]; p]; f[3] = 3; Sort@ Array[f, 950]

CROSSREFS

Cf. A007809, A007810, A099651, A099653, A099654, A099756, A100369.

Sequence in context: A182231 A100110 A095323 * A233393 A233265 A095319

Adjacent sequences: A100367 A100368 A100369 * A100371 A100372 A100373

KEYWORD

base,fini,full,nonn

AUTHOR

Labos Elemer, Nov 30 2004

STATUS

approved