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A274424 Numbers k such that there exists an m for which k = Sum_{j=1..m} (k mod prime(j)).

%I A274424 #17 Feb 11 2021 01:17:48
%S A274424 13,19,48,63,67,76,94,99,123,141,143,150,179,193,247,249,285,339,404,
%T A274424 445,517,693,711,798,969,982,1054,1138,1233,1245,1257,1262,1364,1524,
%U A274424 1531,1569,1613,1694,1701,1743,1745,1928,2018,2070,2114,2224,2339,2461,2770
%N A274424 Numbers k such that there exists an m for which k = Sum_{j=1..m} (k mod prime(j)).
%H A274424 Paolo P. Lava, <a href="/A274424/b274424.txt">Table of n, a(n) for n = 1..1500</a>
%H A274424 Paolo P. Lava, <a href="/A274424/a274424.txt">First 1500 terms with the number of the first primes</a>
%e A274424 48 mod 2 + 48 mod 3 + 48 mod 5 + 48 mod 7 + 48 mod 11 + 48 mod 13 + 48 mod 17 + 48 mod 19 + 48 mod 23 = 0 + 0 + 3 + 6 + 4 + 9 + 14 + 10 + 2 = 48, so 48 is a term.
%p A274424 P:=proc(q) local a,b,k,n; for n from 2 to q do a:=0; b:=2;
%p A274424 while n>a do a:=a+(n mod b); b:=nextprime(b); od;
%p A274424 if n=a then  print(n); fi; od; end: P(10^9);
%Y A274424 Cf. A000040, A024934, A274422, A274423.
%K A274424 nonn,easy
%O A274424 1,1
%A A274424 _Paolo P. Lava_, Jun 21 2016