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A235470 Primes whose base 7 representation also is the base 3 representation of a prime. 1
2, 7, 107, 401, 443, 457, 701, 743, 751, 2417, 2753, 2843, 2851, 3089, 5147, 5153, 5503, 16823, 16921, 17207, 17257, 17551, 19553, 19993, 21617, 21673, 22003, 22303, 33623, 33679, 33721, 34301, 36017, 36373, 36457, 38873, 118057, 118343, 134507, 134857, 135151, 137251, 137593, 140057 (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.

For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.

Since the trailing digit of the base 7 expansion must (like all others) be less than 3, this is a subsequence of A045381.

LINKS

Table of n, a(n) for n=1..44.

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

EXAMPLE

E.g., 7 = 10[7] and 10[3] = 3 both are prime; 107 = 212[7] and 212[3] = 23 both are prime.

PROG

(PARI) is(p, b=3, c=7)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)

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

CROSSREFS

Cf. A065720A036952, A065721 - A065727, A235394, A235395, A089971A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A122524 A229165 A162634 * A072664 A045310 A224445

Adjacent sequences:  A235467 A235468 A235469 * A235471 A235472 A235473

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 12 2014

STATUS

approved

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Last modified August 20 11:27 EDT 2017. Contains 290835 sequences.