A235618 Primes whose base-8 representation also is the base-4 representation of a prime.

2, 3, 11, 19, 67, 89, 137, 211, 523, 593, 641, 659, 1097, 1163, 1627, 1667, 1747, 4177, 4673, 4691, 5323, 5657, 5659, 5779, 5827, 5849, 8209, 8387, 8779, 8849, 9227, 9241, 9283, 9433, 9803, 9817, 9859, 9883, 9929, 12289, 12377, 12433, 12491, 12953, 13003, 13331, 13339, 13441

Offset

1,1

Comments

This sequence is part of the two-dimensional array of sequences based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.

Links

Robert Price, Table of n, a(n) for n = 1..1627

M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Example

E.g., 11 = 13_8 and 13_4 = 7 are both prime.

Prog

(PARI) is(p, b=4, c=8)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 8, 4)&&print1(vector(#d=digits(p, 4), i, 8^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 9)

Crossrefs

Cf. A235633, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Sequence in context: A051083 A051097 A214773 * A076201 A129668 A086791

Adjacent sequences: A235615 A235616 A235617 * A235619 A235620 A235621

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved