A329807 - OEIS

%I #21 Jul 16 2024 08:09:06

%S 126,350,8125,12742,19879,29240,42974,76728,91329,109241,140750,

%T 209222,254681,258272,297423,482958,744901,755169,918601,986174,

%U 1026214,1418606,1515227,1521233,1888216,2082977,2216080,2317257,3510926,4180848,4316417,4330888,4836895

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

%C 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 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 Jianing Song, <a href="/A329807/b329807.txt">Table of n, a(n) for n = 1..243</a> (All terms <= 10^9)

%e 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 (PARI) isA329807(n) = is(n)&&is(n+1)&&is(n+2)&&is(n+3) \\ is() is defined in A055394.

%Y Cf. A055394, A329808, A295787.

%K nonn

%O 1,1

%A _Jianing Song_, Nov 21 2019