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A235615 Primes whose base 5 representation also is the base 4 representation of a prime. 27
2, 3, 13, 41, 43, 61, 181, 191, 263, 281, 283, 331, 383, 431, 443, 463, 641, 643, 661, 881, 911, 1063, 1091, 1291, 1303, 1531, 1693, 2083, 2143, 2203, 2293, 2341, 3163, 3181, 3191, 3253, 3343, 3593, 3761, 3931, 4001, 4093, 4391, 4691, 4793, 5011, 5393, 5413, 5441, 6301 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..50.

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

EXAMPLE

E.g., 13 = 23[5] and 23[4] = 11 both are prime.

PROG

(PARI) is(p, b=4, c=5)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)

(PARI) forprime(p=1, 3e3, is(p, 5, 4)&&print1(vector(#d=digits(p, 4), i, 5^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 5)

CROSSREFS

Cf. A235474, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Sequence in context: A289549 A259261 A141511 * A117528 A264042 A122719

Adjacent sequences:  A235612 A235613 A235614 * A235616 A235617 A235618

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 13 2014

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)