A385243 a(0) = 0 and a(1) = 1 followed by primes p such that (2p)^4 + 1 is prime.

0, 1, 2, 3, 17, 23, 37, 41, 53, 59, 71, 97, 127, 139, 167, 233, 263, 277, 283, 379, 389, 457, 521, 563, 571, 601, 619, 661, 691, 743, 797, 809, 811, 823, 853, 859, 877, 967, 971, 997, 1051, 1063, 1103, 1187, 1277, 1289, 1321, 1367, 1399, 1433, 1451, 1499, 1511, 1523

Offset

0,3

Comments

The initial terms 0 and 1 are included as to form the sequence of noncomposite integers k such that (2k)^4 + 1 is not composite, slightly more complete and/or general than the sequence restricted to primes.

The primes (2p)^4 + 1 with p > 2 are listed in A188717.

Links

James C. McMahon, Table of n, a(n) for n = 0..10000

Formula

a(n) = (A188717(n)-1)^(1/4) / 2, for n > 2.

Mathematica

Join[{0, 1}, Select[Prime[Range[250]], PrimeQ[(2#)^4+1]&]] (* James C. McMahon, Nov 06 2025 *)

Prog

(PARI) concat([0, 1], [p | p<-primes(250), isprime(p^4<<4+1) ])

Crossrefs

Cf. A188717.

Sequence in context: A019388 A228198 A378146 * A023214 A225946 A095688

Adjacent sequences: A385240 A385241 A385242 * A385244 A385245 A385246

Keyword

nonn

Author

M. F. Hasler, Nov 02 2025

Status

approved