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 A293622 #18 Mar 12 2025 10:40:30 %S A293622 561,2701,4371,8911,10585,18721,33153,41041,49141,93961,104653,115921, %T A293622 157641,226801,289941,314821,334153,534061,665281,721801,831405, %U A293622 873181,915981,1004653,1373653,1537381,1755001,1815465,1987021,2035153,2233441,2284453,3059101 %N A293622 Fermat pseudoprimes to base 2 that are triangular. %C A293622 Rotkiewicz proved that this sequence is infinite. %C A293622 Intersection of A001567 and A000217. %C A293622 Supersequence of A290945 (triangular Carmichael numbers). %C A293622 All values of A098025(n)*(2*A098025(n)-1) are terms in this sequence. %C A293622 The corresponding indices of the triangular numbers are 33, 73, 93, 133, 145, 193, 257, 286, 313, 433, 457, 481, 561, 673, 761, 793, 817, ... %H A293622 Amiram Eldar, <a href="/A293622/b293622.txt">Table of n, a(n) for n = 1..10000</a> %H A293622 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_3">Triangular Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 83-125. %H A293622 Andrzej Rotkiewicz, <a href="https://eudml.org/doc/140792">Sur les nombres pseudopremiers triangulaires</a>, Elemente der Mathematik, Vol. 19 (1964), pp. 82-83. %e A293622 2701 = 73 * 74 / 2 = 37 * 73 is in the sequence since it is triangular and composite, and 2^2700 == 1 (mod 2701). %t A293622 t[n_]:=n(n+1)/2; Select[t[Range[3, 10^4]], PowerMod[2, (# - 1), # ] == 1 &] %o A293622 (PARI) forcomposite(c=1, 31*10^5, if(Mod(2, c)^(c-1)==1 && ispolygonal(c, 3), print1(c, ", "))) \\ _Felix Fröhlich_, Oct 14 2017 %Y A293622 Cf. A000217, A001567, A098025, A290945. %K A293622 nonn %O A293622 1,1 %A A293622 _Amiram Eldar_, Oct 13 2017