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.
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.
LINKS
Zak Seidov, Table of n, a(n) for n = 1..1400
EXAMPLE
739 = 1011_9 and 1011_2 = 11 are both prime, so 739 is a term.
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 *)
PROG
(PARI) is(p, b=2, c=9)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(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)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 11 2014
STATUS
approved