A339805 Numbers k such that the sum of decimal digits of k is the sum of primes dividing k+1 (with repetition).

5, 17, 47, 97, 98, 159, 279, 359, 485, 489, 749, 879, 1679, 1979, 2399, 2499, 3968, 5669, 6749, 7199, 7799, 8099, 8639, 9719, 12799, 19199, 25599, 31999, 37499, 39599, 44799, 68599, 78399, 78749, 79379, 94499, 134999, 143999, 146999, 161999, 172799, 175999, 194399, 199679, 209999, 218699, 259999

Offset

1,1

Comments

Numbers k such that A007953(k) = A001414(k+1).

If m is not divisible by 10, A007953(10^k*m-1) = A007953(m) - 1 + 9*k while A001414(10^k*m) = A001414(m) + 7*k. Thus if in addition A001414(m) - A007953(m) is odd and positive, 10^k*m-1 is in the sequence where k = (A001414(m) - A007953(m)+1)/2.

Are there infinitely many terms that do not end in 9?

Links

Robert Israel, Table of n, a(n) for n = 1..156

Example

a(4) = 97 is in the sequence because 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(t -> sod(t) = spf(t+1), [$1..10^6]);

Prog

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

Crossrefs

Cf. A001414, A007953, A063737.

Sequence in context: A003295 A228857 A253427 * A338972 A332358 A011853

Adjacent sequences: A339802 A339803 A339804 * A339806 A339807 A339808

Keyword

nonn,base

Author

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

Status

approved