A175738 Sizes of successive increasing gaps between 2-pseudoprimes.

220, 460, 756, 780, 1140, 1356, 1496, 2000, 3050, 3580, 4532, 4784, 5220, 7140, 12132, 20412, 20650, 22320, 26076, 39424, 42392, 65740, 81252, 87698, 137104, 164448, 203506, 370396, 484140, 491526, 506940, 667908, 682820, 777224, 951114, 1201538

Offset

1,1

Comments

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

References

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..207

Charles R Greathouse IV, Illustration of gap sizes vs. lower end

H. Halberstam and A. Rotkiewicz, A gap theorem for pseudoprimes in arithmetic progression, Acta Arithmetica 13 (1967/1968), pp. 395-404.

Eric Weisstein's World of Mathematics, Fermat Pseudoprime

Index entries for sequences related to pseudoprimes

Formula

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

Crossrefs

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

Sequence in context: A287011 A333929 A157107 * A260203 A184543 A234558

Adjacent sequences: A175735 A175736 A175737 * A175739 A175740 A175741

Keyword

nonn,nice

Author

Charles R Greathouse IV, Aug 28 2010

Status

approved