A235466 Primes whose base-9 representation also is the base-2 representation of a prime.

739, 811, 6571, 59779, 532261, 591301, 4783699, 4789621, 4842109, 4849399, 5314411, 5314501, 5373469, 5374279, 43047541, 43112341, 43113061, 47888821, 47889559, 47895301, 48361861, 48420271, 48420919, 387421219, 387486109, 388011061, 388011709, 392210029, 392262589, 392734981

Offset: 1

Author

M. F. Hasler, Jan 11 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.

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

When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=9, thus a subsequence of A077723.

Examples

			739 = 1011_9 and 1011_2 = 11 are both prime, so 739 is a term.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1400
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

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

Programs

Mathematica

fQ[n_, j_, k_] := Block[{id = IntegerDigits[n, j]}, Max[id] < k && PrimeQ[ FromDigits[ id, k]]]; lst = {}; p = 2; While[p < 4*10^9, If[ fQ[p, 9, 2], AppendTo[lst, p]; Print[p]]; p = NextPrime@ p] (* Robert G. Wilson v, Oct 09 2014 *)
pr9Q[n_]:=Module[{idn9=IntegerDigits[n,9]},Max[idn9]<2&&PrimeQ[ FromDigits[ idn9,2]]]; Select[Prime[Range[21*10^6]],pr9Q] (* Harvey P. Dale, Aug 25 2015 *)

PARI

is(p,b=2,c=9)=vecmax(d=digits(p,c))
				

PARI

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