A023281 Primes that remain prime through 3 iterations of function f(x) = 4x + 3.

2, 109, 179, 571, 677, 977, 1279, 1447, 1747, 1901, 2207, 2671, 3119, 3917, 5011, 5399, 5441, 5569, 5791, 6211, 6607, 7079, 7417, 8369, 8831, 9221, 9697, 9769, 11821, 11897, 12347, 13537, 13669, 13691, 13729, 13781, 13907, 14747, 14851, 15581, 17231, 17497

Offset

1,1

Comments

Primes p such that 4*p+3, 16*p+15 and 64*p+63 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Maple

f:=proc(x) options operator, arrow: 4*x+3 end proc: a:=proc(n) if isprime(n)= true and isprime(f(n))=true and isprime(f(f(n)))=true and isprime(f(f(f(n)))) =true then n else end if end proc: seq(a(n), n=1..20000); # Emeric Deutsch, Jan 01 2008

Mathematica

Select[Prime@ Range@ 2100, Times @@ Boole@ PrimeQ@ Rest@ NestList[4 # + 3 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 19 2016 *)

Prog

(Magma) [n: n in [1..150000] | IsPrime(n) and IsPrime(4*n+3) and IsPrime(16*n+15) and IsPrime(64*n+63)] // Vincenzo Librandi, Aug 04 2010
(PARI) is(n)=isprime(n) && isprime(4*n+3) && isprime(16*n+15) && isprime(64*n+63) \\ Charles R Greathouse IV, Sep 20 2016

Crossrefs

Subsequence of A023213, A023250, and of A095278.

Sequence in context: A372117 A247098 A245056 * A042457 A062656 A173372

Adjacent sequences: A023278 A023279 A023280 * A023282 A023283 A023284

Keyword

nonn

Author

David W. Wilson

Status

approved