A307473 SanD-50 primes: primes p such that p+d is also prime and sum of digits A007953(p(p+d)) = d, with d = 50.

2543, 3137, 3407, 4973, 5147, 5693, 7193, 7523, 7649, 7673, 8243, 8513, 8573, 8627, 9293, 9461, 9497, 9767, 9833, 9857, 9923, 10463, 11279, 11777, 11789, 12107, 12161, 12647, 12917, 12953, 13043, 13127, 13217, 14033, 15137, 15443, 15767, 15773, 16061, 16427, 16553, 16607, 16937, 16943, 17117, 17207, 18047

Offset

1,1

Comments

SanD-d primes exist only for d = 14 + 18*k, k = -1/2, 0, 1, 2, 3, ...

This is the sequence for k = 2. See cross-references for other k and related sequences, in particular the main entry A307479 with further references.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1) = 2543 = A307479(42) = A307480(2) is the smallest SanD-50 prime: 2543 and 2543 + 50 = 2593 both are prime, and the digit sum A007953(2543*2593) = 6+5+9+3+9+9+9 = 50.

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..20000, 6)], 50); # Robert Israel, Apr 10 2019

Prog

(PARI) print_A307473(N, d=50)=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: A234407 A135924 A250686 * A327771 A035876 A072435

Adjacent sequences: A307470 A307471 A307472 * A307474 A307475 A307476

Keyword

nonn,base

Author

M. F. Hasler, Apr 09 2019

Status

approved