

A307480


Smallest SanDd prime p (such that p + d is also prime and digit sum A007953(p(p+d)) = d) with d = 14 + n*18, n >= 0, resp. d = 5 for n = 1.


10




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 SanDd prime.
This sequence lists the smallest SanDd 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

Table of n, a(n) for n=1..7.
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) SanD5 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 SanD14 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 SanD32 prime: 149 and 149 + 32 = 181 both are prime, and the digit sum A007953(149*181) = 2+6+9+6+9 = 32.
a(2) = 2543 = A307473(1) is the smallest SanD50 prime: 2543 and 2543 + 50 = 2593 both are prime, and the digit sum A007953(2543*2593) = 6+5+9+3+9+9+9 = 50.
a(3) = 19961 = A307474(1) is the smallest SanD68 prime: 19961 and 19961 + 68 = 20029 both are prime, and the digit sum A007953(19961*20029) = 3+9+9+7+9+8+8+6+9 = 68.


PROG

(PARI) A307480(n, d=max(14+18*n, 5))=forprime(p=2, , isprime(p+d)&&sumdigits(p*(p+d))==d&&return(p))


CROSSREFS

Cf. A307471  A307478 (d = 14+18k, k=0..7), A307479 (any d: main entry).
Cf. A000040 (primes), A007953 (sum of digits).
Sequence in context: A175525 A069139 A155762 * A062611 A263413 A270585
Adjacent sequences: A307477 A307478 A307479 * A307481 A307482 A307483


KEYWORD

nonn,base,more


AUTHOR

M. F. Hasler, Apr 09 2019


STATUS

approved



