This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329808 #20 Jul 27 2024 19:14:39 %S A329808 9,36,43,72,100,126,127,128,170,196,225,232,264,289,320,350,351,352, %T A329808 359,368,407,424,441,442,485,486,511,512,539,576,632,656,700,703,737, %U A329808 784,792,810,841,848,849,872,908,953,968,1000,1018,1169,1183,1213,1225,1240,1296 %N A329808 Numbers k such that both k and k+1 are sums of a positive square and a positive cube. %C A329808 It is quite easy to give a constructive proof that this sequence is infinite. For example, 64*x^3 + 49*x^2 + 14*x + 1 = (7*x+1)^2 + (4*x)^3 and 64*x^3 + 49*x^2 + 14*x + 2 = (x+1)^2 + (4*x+1)^3. Moreover, if 97*x^2 + 2*x + 1 = y^2, then 64*x^3 + 49*x^2 + 14*x = y^2 + (4*x-1)^3. Obviously there are infinitely many solutions to 97*x^2 + 2*x + 1 = y^2, so there are infinitely many k such that k, k+1 and k+2 are all sums of a positive square and a positive cube. %H A329808 Jianing Song, <a href="/A329808/b329808.txt">Table of n, a(n) for n = 1..10000</a> %e A329808 43 is a term because 43 = 4^2 + 3^3, 44 = 6^2 + 2^3. %o A329808 (PARI) isA329808(n) = is(n)&&is(n+1) \\ is() is defined in A055394. %Y A329808 Cf. A055394, A295787, A329807. %K A329808 nonn %O A329808 1,1 %A A329808 _Jianing Song_, Nov 21 2019