A307472 SanD-32 primes: p and p+d are both prime and digit sum A007953(p*(p+d)) = d, with d=32.

149, 179, 239, 281, 389, 431, 491, 509, 569, 659, 1019, 1031, 1061, 1259, 1289, 1427, 1439, 1901, 2081, 2111, 2129, 2207, 2237, 2309, 2357, 2441, 2657, 2687, 2801, 3137, 3221, 3359, 3527, 3581, 3659, 3701, 3761, 4127, 4241, 4391, 4517, 4691, 4871, 4877, 4937, 5147, 5381, 5387, 5417, 5591, 5657, 5717, 5807, 6011

Offset

1,1

Comments

N. E. Frankel named "S(um)anD(ifference) number" any n such that the sum of digits of n(n+d) equals d, for some d, and SanD primes if in addition, p and p+d are prime.

The only SanD prime with odd d is p = 2, d = 5. All other SanD primes must have d = 14 + 18k, k = 0, 1, 2, 3,...

This is the sequence for k = 1. See A307471 - A307478 for d = 14+18k, k=0..7, A307479 for the union (any d), and A307480 for the smallest SanD-d prime for given d = 14 + 18k, k = -1/2, 0, 1, 2, 3, ...

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(1) = 149 = A307479(10) = A307480(1) is the smallest SanD-32 prime: 149 and 149 + 32 = 181 both are prime, and the digit sum A007953(149*181) = 2+6+9+6+9 = 32.

Maple

sand:= (n, d) -> isprime(n) and isprime(n+d) and convert(convert(n*(n+d), base, 10), `+`)=d:
select(sand, [seq(i, i=5..10000, 6)], 32); # Robert Israel, Apr 10 2019

Prog

(PARI) print_A307472(N, d=32)=forprime(p=2, , isprime(p+d)&&sumdigits(p*(p+d))==d&&!print1(p, ", ")&&!N--&&break)

Crossrefs

Cf. A307471 - A307478 (d = 14+18k, k=0..7), A307479 (any d), A307480 (smallest prime for given d).

Cf. A000040 (primes), A007953 (sum of digits).

Sequence in context: A100723 A316589 A178127 * A209619 A031929 A161487

Adjacent sequences: A307469 A307470 A307471 * A307473 A307474 A307475

Keyword

nonn,base

Author

M. F. Hasler, Apr 09 2019

Status

approved