A339805 - OEIS

%I #17 Feb 06 2021 22:08:44

%S 5,17,47,97,98,159,279,359,485,489,749,879,1679,1979,2399,2499,3968,

%T 5669,6749,7199,7799,8099,8639,9719,12799,19199,25599,31999,37499,

%U 39599,44799,68599,78399,78749,79379,94499,134999,143999,146999,161999,172799,175999,194399,199679,209999,218699,259999

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

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

%C 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.

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

%H Robert Israel, <a href="/A339805/b339805.txt">Table of n, a(n) for n = 1..156</a>

%e 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.

%p sod:= n -> convert(convert(n,base,10),`+`):

%p spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:

%p select(t -> sod(t) = spf(t+1), [$1..10^6]);

%o (PARI) isok(m) = my(f=factor(m+1)); sumdigits(m) == f[, 1]~*f[, 2]; \\ _Michel Marcus_, Dec 18 2020

%Y Cf. A001414, A007953, A063737.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 18 2020