A235617 Primes whose base-7 representation also is the base-4 representation of a prime.

2, 3, 17, 59, 71, 73, 113, 353, 367, 449, 463, 491, 701, 743, 757, 787, 857, 1039, 1151, 1193, 2411, 2423, 2467, 2551, 2843, 3109, 3137, 3209, 3251, 4817, 4903, 5209, 5657, 5839, 5939, 5953, 7211, 7603, 7703, 8009, 8039, 8291, 8387, 16831, 16871, 16927, 17207, 17321, 17837, 19211, 19267, 20261, 20287, 22123, 22303

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..8515

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

Example

E.g., 17 = 23_7 and 23_4 = 11 are both prime.

Prog

(PARI) is(p, b=4, c=7)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 7, 4)&&print1(vector(#d=digits(p, 4), i, 7^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 9)

Crossrefs

Cf. A235634, 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: A106860 A042699 A078983 * A201455 A085874 A055739

Adjacent sequences: A235614 A235615 A235616 * A235618 A235619 A235620

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved