

A082184


The a(n)th triangular number is the sum of the nth 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
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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



