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%I #15 May 31 2020 02:12:56
%S 561,2701,4371,8911,10585,18721,33153,41041,49141,93961,104653,115921,
%T 157641,226801,289941,314821,334153,534061,665281,721801,831405,
%U 873181,915981,1004653,1373653,1537381,1755001,1815465,1987021,2035153,2233441,2284453,3059101
%N Fermat pseudoprimes to base 2 that are triangular.
%C Rotkiewicz proved that this sequence is infinite.
%C Intersection of A001567 and A000217.
%C Supersequence of A290945 (triangular Carmichael numbers).
%C All values of A098025(n)*(2*A098025(n)-1) are terms in this sequence.
%C 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 Amiram Eldar, <a href="/A293622/b293622.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 2701 = 73 * 74 / 2 = 37 * 73 is in the sequence since it is triangular and composite, and 2^2700 == 1 (mod 2701).
%t t[n_]:=n(n+1)/2; Select[t[Range[3, 10^4]], PowerMod[2, (# - 1), # ] == 1 &]
%o (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 Cf. A000217, A001567, A098025, A290945.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 13 2017
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