

A243442


Primes p such that, in base 2, p  digitsum(p) is also a prime.


8



5, 23, 71, 83, 101, 113, 197, 281, 317, 353, 359, 373, 401, 467, 599, 619, 683, 739, 751, 773, 977, 1091, 1097, 1103, 1217, 1223, 1229, 1237, 1283, 1303, 1307, 1429, 1433, 1489, 1553, 1559, 1601, 1607, 1613, 1619, 1699, 1873, 1879, 2039, 2347, 2357, 2389
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OFFSET

1,1


COMMENTS

In all bases b, x = n  digitsum(n) is always divisible by b1, therefore x can be prime only in base 2 and bases b for which b1 is prime. For example, in base 10, n  digitsum(n) is always divisible by 10  1 = 9  see A066568 and A068395. In base 8, 9 = 11, therefore 11  digitsum(11) = 9  2 = 7 is divisible by 7.


LINKS

Anthony Sand, Table of n, a(n) for n = 1..1000


EXAMPLE

5  digitsum(5,base=2) = 5  digitsum(101) = 5  2 = 3.
23  digitsum(10111) = 23  4 = 19.
71  digitsum(1000111) = 71  4 = 67.
83  digitsum(1010011) = 83  4 = 79.
101  digitsum(1100101) = 101  4 = 97.


PROG

(PARI) isok(n) = isprime(n) && isprime(n  hammingweight(n)); \\ Michel Marcus, Jun 05 2014


CROSSREFS

Cf. A243441.
Sequence in context: A084671 A284648 A290187 * A064395 A230497 A138905
Adjacent sequences: A243439 A243440 A243441 * A243443 A243444 A243445


KEYWORD

nonn,base


AUTHOR

Anthony Sand, Jun 05 2014


STATUS

approved



