A235475 Primes whose base-2 representation also is the base-5 representation of a prime.

2, 7, 11, 13, 19, 41, 59, 127, 151, 157, 167, 173, 181, 191, 223, 233, 241, 271, 313, 331, 409, 421, 443, 463, 541, 563, 577, 607, 613, 641, 701, 709, 733, 743, 809, 859, 877, 919, 929, 953, 967, 991, 1021, 1033, 1069, 1087, 1193, 1259, 1373, 1423, 1451, 1453, 1471, 1483, 1493, 1549, 1697, 1753, 1759, 1783, 1787, 1831, 1877, 1979, 1993

Offset

1,1

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Example

7 = 111_2 and 111_5 = 31 are both prime, so 7 is a term.

Mathematica

Select[Prime[Range[400]], PrimeQ[FromDigits[IntegerDigits[#, 2], 5]]&] (* Harvey P. Dale, Jun 15 2019 *)

Prog

(PARI) is(p, b=5, c=2)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ This code is only valid for b>c.

Crossrefs

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

Sequence in context: A140557 A027697 A364470 * A146315 A038892 A019346

Adjacent sequences: A235472 A235473 A235474 * A235476 A235477 A235478

Keyword

nonn,base

Author

M. F. Hasler, Jan 12 2014

Status

approved