|
|
A235478
|
|
Primes whose base-2 representation also is the base-8 representation of a prime.
|
|
3
|
|
|
7, 11, 13, 29, 37, 43, 47, 53, 61, 67, 71, 73, 107, 139, 149, 199, 211, 227, 263, 293, 307, 311, 317, 331, 347, 383, 389, 421, 461, 467, 541, 593, 601, 619, 641, 643, 739, 811, 863, 907, 937, 1061, 1069, 1093, 1117, 1163, 1223, 1283, 1301, 1319, 1321, 1409, 1433, 1439, 1489, 1499, 1523, 1559, 1619, 1697, 1811, 1861, 1879
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
This sequence is part of a two-dimensional array of sequences, given in the LINK, 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.
|
|
LINKS
|
|
|
EXAMPLE
|
11 = 1011_2 and 1011_8 = 521 are both prime, so 11 is a term.
|
|
MATHEMATICA
|
Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 2], 8]]&] (* Harvey P. Dale, Sep 25 2015 *)
|
|
PROG
|
(PARI) is(p, b=8)=isprime(vector(#d=binary(p), i, b^(#d-i))*d~)&&isprime(p)
|
|
CROSSREFS
|
Cf. A235465 ⊂ A077722, A235266, A152079, A235475 - A235479, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|