A235629 Primes whose base-9 representation also is the base-5 representation of a prime.

2, 3, 11, 19, 29, 31, 101, 109, 181, 191, 199, 281, 337, 739, 751, 769, 811, 821, 839, 919, 929, 991, 1459, 1489, 1549, 1721, 1741, 1811, 2269, 2281, 2371, 2389, 2441, 2459, 2531, 2539, 2551, 2953, 3089, 3109, 3251, 3271, 6571, 6599, 6661, 6907, 7309, 7321, 7489, 7537, 8039

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

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 11 = 12_9 and 12_5 = 7 are prime.

Mathematica

pr95Q[n_]:=Module[{idn9=IntegerDigits[n, 9]}, Max[idn9]<5&&PrimeQ[ FromDigits[ idn9, 5]]]; Select[Prime[Range[1100]], pr95Q] (* Harvey P. Dale, Nov 30 2022 *)

Prog

(PARI) is(p, b=5, c=9)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 9, 5)&&print1(vector(#d=digits(p, 5), i, 9^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 5, 9)

Crossrefs

Cf. A235482, 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: A363497 A135206 A368278 * A111802 A213894 A294668

Adjacent sequences: A235626 A235627 A235628 * A235630 A235631 A235632

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved