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

13, 19, 48, 63, 67, 76, 94, 99, 123, 141, 143, 150, 179, 193, 247, 249, 285, 339, 404, 445, 517, 693, 711, 798, 969, 982, 1054, 1138, 1233, 1245, 1257, 1262, 1364, 1524, 1531, 1569, 1613, 1694, 1701, 1743, 1745, 1928, 2018, 2070, 2114, 2224, 2339, 2461, 2770

Offset: 1

Author

Paolo P. Lava, Jun 21 2016

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1500
• Paolo P. Lava, First 1500 terms with the number of the first primes

Crossrefs

Cf. A000040, A024934, A274422, A274423.

Programs

Maple

P:=proc(q) local a,b,k,n; for n from 2 to q do a:=0; b:=2;
while n>a do a:=a+(n mod b); b:=nextprime(b); od;
if n=a then  print(n); fi; od; end: P(10^9);