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%I #14 Apr 10 2019 15:11:07
%S 2543,3137,3407,4973,5147,5693,7193,7523,7649,7673,8243,8513,8573,
%T 8627,9293,9461,9497,9767,9833,9857,9923,10463,11279,11777,11789,
%U 12107,12161,12647,12917,12953,13043,13127,13217,14033,15137,15443,15767,15773,16061,16427,16553,16607,16937,16943,17117,17207,18047
%N SanD-50 primes: primes p such that p+d is also prime and sum of digits A007953(p(p+d)) = d, with d = 50.
%C SanD-d primes exist only for d = 14 + 18*k, k = -1/2, 0, 1, 2, 3, ...
%C 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.
%H Robert Israel, <a href="/A307473/b307473.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%p sand:= (n,d) -> isprime(n) and isprime(n+d) and convert(convert(n*(n+d),base,10),`+`)=d:
%p select(sand, [seq(i,i=5..20000,6)], 50); # _Robert Israel_, Apr 10 2019
%o (PARI) print_A307473(N,d=50)=forprime(p=2,,isprime(p+d)&&sumdigits(p*(p+d))==d&&!print1(p,",")&&!N--&&break)
%Y Cf. A307471 - A307478 (d = 14+18k, k=0..7), A307479 (any d), A307480 (smallest prime for given d).
%Y Cf. A000040 (primes), A007953 (sum of digits).
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Apr 09 2019
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