A274422 -id:A274422 - cp's OEIS frontend

A274423 Let s(n,j) be Sum_{i=1..j} (prime(primepi(n) + i) mod n). Numbers n such that there exists j with s(n,j) = n.

2, 3, 4, 6, 8, 44, 48, 66, 90, 108, 156, 206, 284, 854, 1002, 1188, 1194, 1212, 1320, 2234, 2460, 2792, 3336, 3478, 7096, 7164, 7218, 7236, 7752, 8304, 9164, 10272, 12090, 12594, 13322, 15530, 17038, 17162, 18026, 18212, 20412, 20494, 21966, 23374, 23518, 24664

Offset: 1

Paolo P. Lava, Jun 21 2016

			47 mod 44 + 53 mod 44 + 59 mod 44 + 61 mod 44 = 3 + 9 + 15 + 17 = 44.

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

Cf. A000040, A024934, A274422, A274424.

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

Name corrected by David A. Corneth, Jun 22 2016

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

A274423 Let s(n,j) be Sum_{i=1..j} (prime(primepi(n) + i) mod n). Numbers n such that there exists j with s(n,j) = n.

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