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A082184
The a(n)-th triangular number is the sum of the n-th triangular number and the smallest triangular number possible.
7
3, 6, 10, 6, 8, 28, 13, 10, 13, 18, 21, 16, 15, 26, 136, 21, 23, 40, 21, 23, 28, 38, 27, 31, 28, 28, 61, 36, 38, 496, 53, 36, 43, 36, 61, 46, 41, 44, 106, 51, 53, 91, 45, 49, 58, 78, 66, 52, 54, 53, 112, 66, 55, 58, 78, 62, 73, 98, 101, 76, 67, 106, 166, 66, 83, 142, 71
OFFSET
2,1
COMMENTS
a(n) is triangular if n+1 is triangular. Conjectures: partial maxima of sequence are at index i with value from A068195 and also a(i) - A082183(i) = 1, where i is in A068194.
LINKS
J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020.
MAPLE
a:= proc(n) local h, j; h:= n*(n+1); for j from n+1 do
if issqr(1+4*(j*(j+1)-h)) then return j fi od
end:
seq(a(n), n=2..70); # Alois P. Heinz, Jul 31 2019
MATHEMATICA
a[n_] := Module[{h = n(n+1), j}, For[j = n+1, True, j++, If[IntegerQ[ Sqrt[1 + 4 (j(j+1) - h)]], Return[j]]]];
a /@ Range[2, 70] (* Jean-François Alcover, Jun 05 2020, after Maple *)
PROG
(PARI) for(n=2, 100, t=n*(n+1)/2; for(k=1, 10^9, u=t+k*(k+1)/2; v=floor(sqrt(2*u)); if(v*(v+1)/2==u, print1(v", "); break)))
CROSSREFS
Cf. A000217, A080824, index of second term is in A082183.
Partial maxima have index in A068194.
Sequence in context: A232175 A065234 A333531 * A080817 A139762 A055262
KEYWORD
nonn
AUTHOR
Ralf Stephan, Apr 06 2003
STATUS
approved