OFFSET
-1,1
COMMENTS
If p is a S(um)anD(difference) prime with d = sum of digits of p(p+d), we call it a SanD-d prime.
This sequence lists the smallest SanD-d prime for each possible value of d = {5, 14, 32, 50, 68, ...}, i.e., d = 14 + 18*k with k = -1/2, 0, 1, 2, 3, ...
The sequence appears to be increasing. Is there an index where this is no more true?
LINKS
Freeman J. Dyson, Norman E. Frankel, Anthony J. Guttmann: SanD primes and numbers, arxiv:1904.03573 [math.CA], April 7, 2019
EXAMPLE
a(-1) = 2 is the smallest (and only) SanD-5 prime: 2 and 2 + 5 = 7 both are prime, and the digit sum A007953(2*7) = 1 + 4 = 5.
All other SanD primes must have gap and sum (of digits of the product) d = 14 + 18*k, k = 0, 1, 2, ... (corresponding to the index in this sequence):
a(0) = 5 is the smallest SanD-14 prime: 5 and 5 + 14 = 19 both are prime and the digit sum A007953(5*19) = 9 + 5 = 14.
a(1) = 149 = A307472(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.
PROG
(PARI) A307480(n, d=max(14+18*n, 5))=forprime(p=2, , isprime(p+d)&&sumdigits(p*(p+d))==d&&return(p))
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
M. F. Hasler, Apr 09 2019
STATUS
approved