A235621 Primes whose base-9 representation also is the base-7 representation of a prime.

2, 3, 5, 13, 23, 29, 37, 47, 59, 103, 109, 131, 167, 173, 181, 199, 211, 263, 283, 379, 419, 509, 541, 733, 787, 821, 859, 911, 919, 983, 1013, 1063, 1091, 1093, 1171, 1487, 1499, 1543, 1549, 1559, 1567, 1571, 1667, 1669, 1733, 1783, 1787, 1913, 1993, 2237, 2287, 2351, 2381, 2477, 2621

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..14672

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

Example

E.g., 13 = 14_9 and 14_7 = 11 are both prime.

Prog

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

Crossrefs

Cf. A231479, 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: A142881 A163159 A048736 * A193300 A215310 A087898

Adjacent sequences: A235618 A235619 A235620 * A235622 A235623 A235624

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved