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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 (list; graph; refs; listen; history; text; internal format)
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

Alois P. Heinz, Table of n, a(n) for n = 2..65536

J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000, 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

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

Adjacent sequences:  A082181 A082182 A082183 * A082185 A082186 A082187

KEYWORD

nonn

AUTHOR

Ralf Stephan, Apr 06 2003

STATUS

approved

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Last modified May 28 15:33 EDT 2020. Contains 334684 sequences. (Running on oeis4.)