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A082183 Smallest k>0 such that T(n)+T(k)=T(m), for some m, T(i) being the triangular numbers, n>1. 9
2, 5, 9, 3, 5, 27, 10, 4, 8, 14, 17, 9, 5, 21, 135, 12, 14, 35, 6, 9, 17, 30, 12, 18, 10, 7, 54, 21, 23, 495, 42, 14, 26, 8, 49, 27, 15, 20, 98, 30, 32, 80, 9, 19, 35, 62, 45, 17, 20, 14, 99, 39, 10, 18, 54, 24, 44, 78, 81, 45, 25, 85, 153, 11, 50, 125, 20, 29, 53, 94, 97 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 2..10000

MAPLE

f:= proc(n) local e, t, te;

     t:= n*(n+1);

     e:= padic:-ordp(t, 2);

     te:= 2^e;

     min(map(d -> (abs(te*d-t/(te*d))-1)/2, numtheory:-divisors(t/te)) minus {0}):

map(f, [$2..100]); # Robert Israel, Sep 15 2017

MATHEMATICA

Table[SelectFirst[Range[10^3], Function[m, PolygonalNumber@ Floor@ Sqrt[2 m] == m][PolygonalNumber[n] + PolygonalNumber[#]] &], {n, 2, 72}] (* Michael De Vlieger, Sep 19 2017, after Maple by Robert Israel *)

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(k", "); break)))

(Python)

from __future__ import division

from sympy import divisors

def A082183(n):

    t = n*(n+1)

    ds = divisors(t)

    for i in range(len(ds)//2-2, -1, -1):

        x = ds[i]

        y = t//x

        a, b = divmod(y-x, 2)

        if b:

            return a

    return -1 # Chai Wah Wu, Sep 12 2017

CROSSREFS

Cf. A000217, A072522, values of m are in A082184.

Sequence in context: A248934 A011432 A324835 * A111474 A111761 A021798

Adjacent sequences:  A082180 A082181 A082182 * A082184 A082185 A082186

KEYWORD

nonn

AUTHOR

Ralf Stephan, Apr 06 2003

STATUS

approved

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Last modified January 26 11:13 EST 2020. Contains 331279 sequences. (Running on oeis4.)