A023305 Primes that remain prime through 4 iterations of function f(x) = 2x + 7.

293, 2063, 4583, 9203, 14723, 20123, 25733, 29453, 40253, 54713, 76103, 97523, 99833, 109433, 138683, 149993, 158243, 196853, 199403, 218873, 253103, 297623, 379913, 416963, 445463, 468113, 508073, 551963, 562403, 564713, 574703, 583733

Offset

1,1

Comments

Primes p such that 2*p+7, 4*p+21, 8*p+49 and 16*p+105 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

John Cerkan, Table of n, a(n) for n = 1..10000

Formula

a(n) == 3 (mod 10). - John Cerkan, Oct 04 2016

Mathematica

rp4Q[n_]:=AllTrue[Rest[NestList[2#+7&, n, 4]], PrimeQ]; Select[Prime[Range[ 50000]], rp4Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 30 2020 *)

Prog

(Magma) [n: n in [1..1000000] | IsPrime(n) and IsPrime(2*n+7) and IsPrime(4*n+21) and IsPrime(8*n+49) and IsPrime(16*n+105)] // Vincenzo Librandi, Aug 04 2010

Crossrefs

Subsequence of A023206, A023244, A023275, and A105760.

Sequence in context: A251674 A217182 A109562 * A109182 A342874 A241047

Adjacent sequences: A023302 A023303 A023304 * A023306 A023307 A023308

Keyword

nonn

Author

David W. Wilson

Status

approved