The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A235461 Primes whose base-4 representation also is the base 2-representation of a prime. 63
 5, 17, 257, 277, 337, 1093, 1109, 1297, 1361, 4357, 5189, 16453, 16657, 16661, 17489, 17669, 17681, 17749, 21521, 21569, 21589, 65537, 65557, 65617, 65809, 66821, 70657, 70981, 70997, 81937, 82241, 83221, 83269, 86017, 86357, 87317 (list; graph; refs; listen; history; text; internal format)
 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=4, thus a subsequence of A077718 and therefore also of A000695, the Moser-de Bruijn sequence. LINKS Table of n, a(n) for n=1..36. M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime EXAMPLE 5 = 11_4 and 11_2 = 3 are both prime, so 5 is a term. 17 = 101_4 and 101_2 = 5 are both prime, so 17 is a term. PROG (PARI) is(p, b=2, c=4)=vecmax(d=digits(p, c))

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 12:15 EDT 2023. Contains 365501 sequences. (Running on oeis4.)