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Sizes of successive increasing gaps between 2-pseudoprimes.
4

%I #16 Feb 16 2025 08:33:12

%S 220,460,756,780,1140,1356,1496,2000,3050,3580,4532,4784,5220,7140,

%T 12132,20412,20650,22320,26076,39424,42392,65740,81252,87698,137104,

%U 164448,203506,370396,484140,491526,506940,667908,682820,777224,951114,1201538

%N Sizes of successive increasing gaps between 2-pseudoprimes.

%C Rotkiewicz proves that a(n) < A175736(n)^2, and that the exponent can be replaced by 1 + epsilon for large enough n.

%D A. Rotkiewicz, "Les intervalles contenants les nombres pseudopremiers", Rendiconti del Circolo Matematico di Palermo, Series 2, 14 (1965), pp. 278-280.

%H Charles R Greathouse IV, <a href="/A175738/b175738.txt">Table of n, a(n) for n = 1..207</a>

%H Charles R Greathouse IV, <a href="/A175738/a175738.png">Illustration of gap sizes vs. lower end</a>

%H H. Halberstam and A. Rotkiewicz, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa13/aa13124.pdf">A gap theorem for pseudoprimes in arithmetic progression</a>, Acta Arithmetica 13 (1967/1968), pp. 395-404.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatPseudoprime.html">Fermat Pseudoprime</a>

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%F a(n) = A175737(n) - A175736(n).

%Y Cf. A001567 (2-pseudoprimes), A175736 (lower end), A175737 (upper end).

%K nonn,nice,changed

%O 1,1

%A _Charles R Greathouse IV_, Aug 28 2010