A235638 - OEIS

A235638

Primes whose base-8 representation also is the base-6 representation of a prime.

2, 3, 5, 13, 17, 29, 37, 41, 73, 97, 109, 137, 149, 173, 193, 197, 229, 233, 281, 293, 337, 521, 541, 557, 601, 613, 617, 673, 677, 733, 797, 877, 1033, 1061, 1069, 1117, 1129, 1217, 1237, 1301, 1321, 1381, 1549, 1553, 1609, 1621, 1693, 1733, 1889, 1901, 2069, 2137, 2221, 2273, 2309

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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..11493

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

EXAMPLE

E.g., 13 = 15_8 and 15_6 = 11 are both prime.

PROG

(PARI) is(p, b=6, c=8)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)

(PARI) forprime(p=1, 3e3, is(p, 8, 6)&&print1(vector(#d=digits(p, 6), i, 8^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 6, 8)

CROSSREFS

Cf. A235631, 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: A215355 A242752 A215813 * A227829 A231481 A284669

Adjacent sequences: A235635 A235636 A235637 * A235639 A235640 A235641

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 13 2014

STATUS

approved