A274423 -id:A274423 - cp's OEIS frontend

A274422 Numbers m such that there exists a j for which m = Sum_{k=1..j} (m mod k), where k runs through the largest j primes less than m.

13, 17, 20, 23, 24, 34, 40, 82, 126, 200, 612, 1154, 1692, 2434, 2806, 3060, 3142, 4052, 4460, 4596, 5020, 5908, 6424, 7304, 7596, 8030, 8040, 9044, 11398, 12254, 12914, 13412, 13716, 16006, 16800, 18560, 22438, 23140, 24424, 24746, 25706, 28318, 29272, 30580

Offset: 1

Paolo P. Lava, Jun 21 2016

			13 mod 11 + 13 mod 7 + 13 mod 5 + 13 mod 3 + 13 mod 2 = 2 + 6 + 3 + 1 + 1 = 13;
40 mod 37 + 40 mod 31 + 40 mod 29 + 40 mod 23 = 3 + 9 + 11 + 17 = 40.

Paolo P. Lava, Table of n, a(n) for n = 1..250
Paolo P. Lava, First 200 terms with the number of primes j

Cf. A000040, A024934, A274423, A274424.

P:=proc(q) local a,b,k,n; for n from 3 to q do a:=0; b:=prevprime(n);
while n>a do a:=a+(n mod b); if b>2 then b:=prevprime(b); else break; fi; od;
if n=a then print(n); fi; od; end: P(10^9);

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

Original entry on oeis.org

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

Paolo P. Lava, Jun 21 2016

			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.

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

Cf. A000040, A024934, A274422, A274423.

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);

cp's OEIS Frontend

A274422 Numbers m such that there exists a j for which m = Sum_{k=1..j} (m mod k), where k runs through the largest j primes less than m.

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