A235477 Primes whose base-2 representation also is the base-7 representation of a prime.

2, 31, 47, 59, 103, 107, 173, 179, 181, 199, 211, 227, 229, 233, 367, 409, 443, 463, 487, 701, 743, 757, 823, 827, 877, 911, 919, 967, 1009, 1123, 1163, 1291, 1321, 1367, 1373, 1447, 1493, 1571, 1583, 1597, 1609, 1627, 1657, 1669, 1721, 1831, 1933, 1987

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.

A subsequence of A027697, A015919, A197636 (conjectural).

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

31 = 11111_2 and 11111_7 = 2801 are both prime, so 31 is a term.

Mathematica

Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 2], 7]]&] (* Harvey P. Dale, May 08 2021 *)

Prog

(PARI) is(p, b=7)=isprime(vector(#d=binary(p), i, b^(#d-i))*d~)&&isprime(p)

Crossrefs

Cf. A235464 ⊂ A077721, A235475, A152079, A235266, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A207973 A193423 A241484 * A370157 A129900 A262834

Adjacent sequences: A235474 A235475 A235476 * A235478 A235479 A235480

Keyword

nonn,base

Author

M. F. Hasler, Jan 12 2014

Status

approved