A235478 Primes whose base-2 representation also is the base-8 representation of a prime.

7, 11, 13, 29, 37, 43, 47, 53, 61, 67, 71, 73, 107, 139, 149, 199, 211, 227, 263, 293, 307, 311, 317, 331, 347, 383, 389, 421, 461, 467, 541, 593, 601, 619, 641, 643, 739, 811, 863, 907, 937, 1061, 1069, 1093, 1117, 1163, 1223, 1283, 1301, 1319, 1321, 1409, 1433, 1439, 1489, 1499, 1523, 1559, 1619, 1697, 1811, 1861, 1879

Offset: 1

Author

M. F. Hasler, Jan 12 2014

Keywords

• nonn
• base

Comments

This sequence is part of a two-dimensional array of sequences, given in the LINK, 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.

For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.

Appears to be a subsequence of A050150, A062090 and A216285.

Examples

			11 = 1011_2 and 1011_8 = 521 are both prime, so 11 is a term.
		

Links

• Robert Price, Table of n, a(n) for n = 1..2265
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Cf. A235465 ⊂ A077722, A235266, A152079, A235475 - A235479, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.

Programs

Mathematica

Select[Prime[Range[300]],PrimeQ[FromDigits[IntegerDigits[#,2],8]]&] (* Harvey P. Dale, Sep 25 2015 *)

PARI

is(p,b=8)=isprime(vector(#d=binary(p),i,b^(#d-i))*d~)&&isprime(p)