cp's OEIS Frontend

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.

A016045 a(n) is the smallest prime p(k) such that the gaps between the primes p(k), p(k+1), p(k+2), ..., p(k+n) are 2, 4, 6, ... 2n.

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%I A016045 #31 Nov 17 2021 13:24:45
%S A016045 3,5,17,347,13901,128981,128981,113575727,2426256797,137168442221,
%T A016045 4656625081181,101951758179851,484511389338941,221860944705726407
%N A016045 a(n) is the smallest prime p(k) such that the gaps between the primes p(k), p(k+1), p(k+2), ..., p(k+n) are 2, 4, 6, ... 2n.
%D A016045 Steven Kahan, 2-4-6-8...Prime Gaps That Appreciate, J. Rec. Math., Vol. 25 #1, pp. 44-46, 1993
%F A016045 a(n) = min{x : x = prime; {x + k + k^2} = primes following x for k=1, .., n}
%e A016045 Consider consecutive primes 347, 349, 353, 359, 367. The gaps are 2, 4, 6, 8, so a(4)=347.
%Y A016045 Cf. A263049.
%K A016045 nonn,more
%O A016045 1,1
%A A016045 _Robert G. Wilson v_
%E A016045 Corrected and extended by _Jud McCranie_, Jun 24 2000
%E A016045 a(11)-a(13) from _Dmitry Petukhov_, Oct 03 2015
%E A016045 a(14) from _Dmitry Petukhov_, Jul 06 2016