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 A321868 Fermat pseudoprimes to base 2 that are octagonal. 1
 341, 645, 2465, 2821, 4033, 5461, 8321, 15841, 25761, 31621, 68101, 83333, 162401, 219781, 282133, 348161, 530881, 587861, 653333, 710533, 722261, 997633, 1053761, 1082401, 1193221, 1246785, 1333333, 1357441, 1398101, 1489665, 1584133, 1690501, 1735841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite. Intersection of A001567 and A000567. The corresponding indices of the octagonal numbers are 11, 15, 29, 31, 37, 43, 53, 73, 93, 103, 151, 167, 233, 271, 307, 341, 421, 443, 467, 487, 491, 577, 593, 601, 631, 645, 667, 673, 683, 705, 727, 751, 761, 901, 911, 919, 991, ... First differs from A216170 at n = 505. LINKS Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259. Wikipedia, Schinzel's Hypothesis H. MATHEMATICA oct[n_]:=n(3n-2); Select[oct[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &] PROG (PARI) isok(n) = (n>1) && ispolygonal(n, 8) && !isprime(n) && (Mod(2, n)^n==2); \\ Daniel Suteu, Nov 29 2018 CROSSREFS Cf. A000567, A001567, A216170, A293623, A293624, A321869. Sequence in context: A215326 A153508 A216170 * A175736 A179839 A172255 Adjacent sequences:  A321865 A321866 A321867 * A321869 A321870 A321871 KEYWORD nonn AUTHOR Amiram Eldar, Nov 20 2018 STATUS approved

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Last modified April 23 18:15 EDT 2019. Contains 322387 sequences. (Running on oeis4.)