A235619 Primes whose base-9 representation also is the base-4 representation of a prime.

2, 3, 109, 181, 271, 829, 919, 1549, 1567, 6661, 6733, 6823, 8101, 8191, 8263, 13933, 14851, 15319, 22123, 59149, 59221, 59239, 59797, 59887, 61507, 65629, 65701, 72253, 72901, 73819, 118189, 118927, 119827, 124669, 125407, 126127, 126307, 132679, 132859

Offset: 1

Author

M. F. Hasler, Jan 13 2014

Keywords

• nonn
• base

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.

Examples

			E.g., 109 = 131_9 and 131_4 = 29 are both prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..1296
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Cf. A235481, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Programs

PARI

is(p,b=4,c=9)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,3e3,is(p,9,4)&&print1(vector(#d=digits(p,4),i,9^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,4,9)