A235616 Primes whose base-6 representation also is the base-4 representation of a prime.

2, 3, 7, 19, 37, 79, 127, 229, 307, 487, 523, 547, 727, 733, 757, 1297, 1423, 1549, 1567, 1627, 1747, 1777, 2647, 2683, 2713, 2857, 2887, 3067, 3361, 3889, 3943, 4003, 4153, 4441, 4651, 4663, 7789, 7867, 8209, 8263, 8293, 8317, 8443, 8467, 9109, 9157, 9343, 9547, 9733

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..24874

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

Example

E.g., 7 = 11_6 and 11_4 = 5 are both prime.

Prog

(PARI) is(p, b=4, c=6)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 6, 4)&&print1(vector(#d=digits(p, 4), i, 6^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 6)

Crossrefs

Cf. A235624, 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: A172461 A253971 A291339 * A257551 A091410 A069051

Adjacent sequences: A235613 A235614 A235615 * A235617 A235618 A235619

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved