cp's OEIS Frontend

A329807 Numbers k such that k, k+1, k+2 and k+3 are all sums of a positive square and a positive cube.

%I A329807 #21 Jul 16 2024 08:09:06
%S A329807 126,350,8125,12742,19879,29240,42974,76728,91329,109241,140750,
%T A329807 209222,254681,258272,297423,482958,744901,755169,918601,986174,
%U A329807 1026214,1418606,1515227,1521233,1888216,2082977,2216080,2317257,3510926,4180848,4316417,4330888,4836895
%N A329807 Numbers k such that k, k+1, k+2 and k+3 are all sums of a positive square and a positive cube.
%C A329807 It is known that there are infinitely many k such that k, k+1, k+2 are all sums of a positive square and a positive cube (see A055394 and A295787). It is natural to ask if this sequence is infinite. There are 243 members here below 10^9.
%C A329807 There are 2 pairs of consecutive numbers below 10^9: (16597502, 16597503) and (593825496, 593825497). Are there infinitely many k such that k, k+1, k+2, k+3 and k+4 are all sums of a positive square and a positive cube?
%H A329807 Jianing Song, <a href="/A329807/b329807.txt">Table of n, a(n) for n = 1..243</a> (All terms <= 10^9)
%e A329807 350 is here because 350 = 15^2 + 5^3, 351 = 18^2 + 3^3, 352 = 3^2 + 7^3 and 353 = 17^3 + 4^3.
%o A329807 (PARI) isA329807(n) = is(n)&&is(n+1)&&is(n+2)&&is(n+3) \\ is() is defined in A055394.
%Y A329807 Cf. A055394, A329808, A295787.
%K A329807 nonn
%O A329807 1,1
%A A329807 _Jianing Song_, Nov 21 2019