A287116 Nonsquare integers that cannot be represented in the form 4M-d, where (a*b)|M and d|(a+b) for some positive integers a,b.

288, 336, 4545

Offset

1,1

Comments

If there are no more terms, the Erdos-Straus conjecture would follow.

This sequence together with the squares (A000290) and E(4) form a partition of the nonnegative integers. That is, this sequence gives nonsquare non-elements of E(4) (see Dubickas and Novikas, 2012).

There are no other terms below 2*10^9.

Links

Table of n, a(n) for n=1..3.

A. Dubickas, A. Novikas, On integers expressible by some special linear form, Acta Math. Univ. Comenianae LXXXI:2 (2012), 203-209.

Wikipedia, Erdos-Straus conjecture.

Crossrefs

Cf. A073101, A075245, A075246, A075247, A075248, A292581, A192787, A292624, A192789.

Sequence in context: A214301 A296902 A371948 * A345553 A345807 A244196

Adjacent sequences: A287113 A287114 A287115 * A287117 A287118 A287119

Keyword

bref,nonn,hard,more

Author

Max Alekseyev, May 19 2017

Status

approved