

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


CROSSREFS

Cf. A065720 ⊂ A036952, A065721  A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707  A091924, A235461  A235482. See the LINK for further crossreferences.
Sequence in context: A229165 A307329 A162634 * A072664 A045310 A224445
Adjacent sequences: A235467 A235468 A235469 * A235471 A235472 A235473


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 12 2014


STATUS

approved



