A338972 Primes p such that the sum of decimal digits of p is the sum of primes dividing p+1 (with repetition).

5, 17, 47, 97, 359, 1979, 2399, 5669, 9719, 12799, 79379, 134999, 143999, 161999, 199679, 671999, 679999, 890999, 967999, 974999, 1249999, 3455999, 3583999, 3644999, 4687499, 4976639, 5279999, 5375999, 6298559, 8774999, 16839899, 24959999, 26459999, 29567999, 45359999, 48383999, 68849999

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..63

Example

a(4) = 97 is in the sequence because 97 is prime, the sum of digits of 97 is 9+7 = 16 and the sum of primes dividing 98=2*7*7 is 2+7+7 = 16.

Maple

sod:= n -> convert(convert(n, base, 10), `+`):
spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
select(p -> sod(p) = spf(p+1), [seq(ithprime(i), i=1..10^5)]);

Prog

(PARI) isok(p) = if (isprime(p), my(f=factor(p+1)); sumdigits(p) == f[, 1]~*f[, 2]); \\ Michel Marcus, Dec 18 2020

Crossrefs

Primes in A339805.

Cf. A001414, A007953.

Sequence in context: A228857 A253427 A339805 * A332358 A011853 A215053

Adjacent sequences: A338969 A338970 A338971 * A338973 A338974 A338975

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Dec 18 2020

Status

approved