A262744 Remainder when sum of first n primes is divided by n-th triangular number.

0, 2, 4, 7, 13, 20, 2, 5, 10, 19, 28, 41, 56, 71, 88, 109, 134, 159, 188, 9, 19, 32, 46, 63, 85, 108, 130, 153, 175, 198, 232, 267, 305, 342, 386, 429, 475, 524, 574, 627, 683, 738, 800, 861, 923, 984, 1054, 1133, 1213, 17, 46, 77, 106, 141, 178

Offset

1,2

Comments

Sequence is interesting because a(n)-a(n-1) < 0 in certain points such as n=7 and n=20, although a(n)-a(n-1) > 0 for other points, generally.

Old name was: a(n) = (Sum_{k=1..n} prime(k)) mod (Sum_{k=1..n} k).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(n) = (Sum_{k=1..n} prime(k)) mod (n*(n+1)/2).

a(n) = A007504(n) mod A000217(n).

Example

a(1) = prime(1) mod 1 = 0.
a(2) = (prime(1) + prime(2)) mod (1+2) = 2.
a(3) = (prime(1) + prime(2) + prime(3)) mod (1+2+3) = 4.
a(4) = (prime(1) + prime(2) + prime(3) + prime(4)) mod (1+2+3+4) = 7.

Maple

s:= proc(n) option remember; ithprime(n)+`if`(n>1, s(n-1), 0) end:
a:= n-> irem(s(n), n*(n+1)/2):
seq(a(n), n=1..70);  # Alois P. Heinz, Oct 01 2015

Mathematica

Table[Mod[Sum[Prime@ k, {k, n}], Sum[k, {k, n}]], {n, 60}] (* Michael De Vlieger, Sep 30 2015 *)
Module[{nn=60, pr, tr}, pr=Accumulate[Prime[Range[nn]]]; tr=Accumulate[ Range[ nn]]; Mod[#[[1]], #[[2]]]&/@Thread[{pr, tr}]] (* Harvey P. Dale, Aug 02 2020 *)

Prog

(PARI) a(n) = sum(k=1, n, prime(k)) % (n*(n+1)/2);
vector(500, n, a(n))

Crossrefs

Cf. A007504, A000217, A090396.

Sequence in context: A002466 A162842 A164901 * A359516 A347703 A112997

Adjacent sequences: A262741 A262742 A262743 * A262745 A262746 A262747

Keyword

nonn,easy,look

Author

Altug Alkan, Sep 29 2015

Extensions

New name from Altug Alkan, Feb 06 2017, following a suggestion from N. J. A. Sloane

Status

approved