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 A378245 #38 Dec 08 2024 13:07:11 %S A378245 1,36,1225,9801,40755,41616,121771,297045,631125,1212751,1413721, %T A378245 2158695,3617601,5773825,8851275,13117251,18886285,26523981,36450855, %U A378245 48024900,49146175,65151801,85076025,94109401,109597411,139468635,175520325,218664901,269900415,330314391 %N A378245 Numbers that are both k-gonal and (k+1)-gonal for some k >= 3. %e A378245 a(2) = 36 is both the 8th triangular and the 6th square number. %e A378245 a(3) = 1225 is both the 49th triangular and the 35th square number. %e A378245 a(5) = 40755 is both the 165th pentagonal number and the 143th hexagonal number. %o A378245 (PARI) upto(limit) = my(terms=List(1)); for(k=3, oo, my(found=0); for(n=2, oo, my(a = (2*n - 1)^2, b = (4*n*(3*n - 5) + 6), c = (8*(n-1)^2 + 1), s = (a*k^2 - b*k + c), v = n * (n*k - k - 2*n + 4) / 2); if(issquare(s), my(t = sqrtint(s) + k - 3); if(t % (2*(k-1)) == 0, listput(terms, v); found += 1)); if(v >= limit, break)); if(found == 0, break)); Vec(vecsort(terms)); \\ _Daniel Suteu_, Dec 08 2024 %Y A378245 Cf. A057145, A342300. %Y A378245 Cf. A001110, A036353, A046180, A048903, A048906, A048924 and A203627 (subsequences). %Y A378245 The subdiagonal of A189216 is also a subsequence. %K A378245 nonn %O A378245 1,2 %A A378245 _Kelvin Voskuijl_, Nov 20 2024 %E A378245 a(12)-a(30) from _Pontus von Brömssen_, Dec 07 2024