A114033 Group the triangular numbers so that the n-th group sum is a multiple of n. 1, (3, 6, 10, 15), (21), (28), (36, 45, 55, 66, 78), (91, 105, 120, 136, 153, 171, 190), ... Sequence contains the number of terms in the n-th group.

1, 4, 1, 1, 5, 7, 1, 3, 17, 3, 1, 8, 11, 5, 1, 32, 1, 17, 19, 2, 19, 11, 16, 8, 19, 4, 19, 2, 29, 25, 7, 64, 9, 2, 14, 2, 37, 19, 26, 30, 12, 28, 10, 22, 1, 21, 3, 19, 49, 25, 17, 104, 53, 8, 11, 112, 19, 58, 29, 1, 61, 124, 35, 11, 9, 44, 8, 34, 46, 15, 69, 54, 73, 37, 1, 152, 77, 65

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Maple

A000217 := proc(n) option remember ; n*(n+1)/2 ; end: A114033 := proc(n) local strt, su, len, i; strt := 1 ; for su from 1 to n do len := 1; while add( A000217(strt+i), i=0..len-1) mod su <> 0 do len := len+1 ; od ; if su = n then RETURN(len) ; else strt := strt+len ; fi ; od ; end: for n from 1 to 80 do printf("%d, ", A114033(n)) ; od ; # R. J. Mathar, May 10 2007

Mathematica

t[n_] := n(n+1)/2;
a[n_] := Module[{strt, su, len}, strt = 1; For[su = 1, True, su++, len = 1; While[Mod[Sum[t[strt + i], {i, 0, len - 1}], su] != 0, len++]; If[su == n, Return[len], strt += len]]];
Table[a[n], {n, 1, 78}] (* Jean-François Alcover, Aug 01 2023, after R. J. Mathar *)

Crossrefs

Cf. A114031, A114032.

Sequence in context: A174037 A173077 A131239 * A334426 A209417 A267990

Adjacent sequences: A114030 A114031 A114032 * A114034 A114035 A114036

Keyword

nonn

Author

Amarnath Murthy, Nov 13 2005

Extensions

More terms from R. J. Mathar, May 10 2007

Status

approved