A235472 Primes whose base-9 representation also is the base-3 representation of a prime.

2, 11, 19, 83, 101, 163, 173, 739, 811, 821, 829, 911, 1549, 1559, 1621, 6563, 6581, 6661, 6733, 8111, 8191, 13933, 14753, 59069, 59141, 59779, 59797, 59951, 60589, 60607, 65629, 65701, 66359, 67079, 67231, 72271, 72353, 72901, 118189, 119557, 119657, 124669, 124823, 125399

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 all digits of the base 9 expansion are less than 3, this is a subsequence of A037314.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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

Example

Both 17 = 21_9 and 21_3 = 7 are prime.

Prog

(PARI) is(p, b=3, c=9)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 2e3, is(p, 9, 3)&&print1(vector(#d=digits(p, 3), i, 9^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 3, 9)

Crossrefs

Cf. A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A067931 A186267 A067660 * A217308 A105076 A103200

Adjacent sequences: A235469 A235470 A235471 * A235473 A235474 A235475

Keyword

nonn,base

Author

M. F. Hasler, Jan 12 2014

Status

approved