

A238018


Least k such that the sum triangular(k) + triangular(k+1) +...+ triangular(k+n1) is a triangular number, or 1 if no such k exists.


1



0, 0, 1, 0, 2, 1, 4, 1, 0, 12, 14, 1, 11, 1, 1, 76, 3, 28, 1, 1, 0, 33, 1, 1, 52, 22, 4, 29, 11, 13, 5, 1, 1, 1, 0, 74, 1, 3, 1, 83, 1, 1, 76, 1006, 1, 1, 518, 1, 150, 1, 1, 103, 133, 51, 14, 45, 19, 1, 5, 1
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OFFSET

1,5


LINKS

Table of n, a(n) for n=1..60.


EXAMPLE

a(5) = 2 because 2 is the least integer such that the sum of 5 consecutive triangular numbers starting with triangular(2) is a triangular number: 55 = 3+6+10+15+21.
a(7) = 4 because 4 is the least integer such that the sum of 7 consecutive triangular numbers starting with triangular(4) is a triangular number: 210 = 10+15+21+28+36+45+55.


MATHEMATICA

s[n_, k_] := n*(3*k^2 + 3*k*n + n^2  1)/6; a[1] = 0; a[n_] := Module[{r}, r = Reduce[ k >= 0 && m >= 0 && 8*s[n, k] + 1 == m^2 , {k, m}, Integers] /. C[1] > 1 // FullSimplify; If[r === False, 1, k /. {ToRules[r]} // Min]]; Table[a[n], {n, 1, 60}] (* JeanFrançois Alcover, Feb 26 2014 *)


CROSSREFS

Cf. A000217, A129803, A238017.
Sequence in context: A117971 A220420 A190616 * A131642 A070674 A070668
Adjacent sequences: A238015 A238016 A238017 * A238019 A238020 A238021


KEYWORD

sign


AUTHOR

Alex Ratushnyak, Feb 17 2014


EXTENSIONS

More terms from JeanFrançois Alcover, Feb 26 2014


STATUS

approved



