A235636 Primes whose base-6 representation is also the base-7 representation of a prime.

2, 3, 5, 17, 47, 71, 97, 101, 131, 157, 173, 191, 211, 251, 257, 277, 307, 311, 353, 367, 401, 421, 461, 487, 491, 563, 577, 601, 631, 643, 647, 683, 701, 743, 751, 761, 853, 857, 907, 911, 937, 953, 983, 1021, 1033, 1087, 1103, 1193, 1201, 1259, 1277, 1289, 1327, 1451, 1471, 1571, 1583, 1597, 1601, 1747, 1831, 1907, 1933

Offset: 1

Author

M. F. Hasler, Jan 13 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.

Examples

			17 = 25_6 and 25_7 = 19 are both prime.
		

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

Crossrefs

Cf. A235637, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Programs

Mathematica

Select[Prime[Range[300]],PrimeQ[FromDigits[IntegerDigits[#,6],7]]&] (* Harvey P. Dale, Sep 17 2017 *)

PARI

is(p,b=7,c=6)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.