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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.

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A273595 Least q > 0 such that min { x >= 0 | q + prime(n)*x + x^2 is composite } is a (local) maximum, cf. A273756 & A273770.

Original entry on oeis.org

43, 47, 53, 71, 83, 113, 131, 173, 251, 281, 383, 461, 503, 593, 743, 73361, 73421, 3071069, 15949847, 76553693, 2204597, 1842719, 246407807, 986578883, 73975907, 4069235123, 1244414939, 25213427, 656856899, 30641069183, 8221946477, 41730358853, 10066886927, 285340609997, 6232338461
Offset: 2

Views

Author

M. F. Hasler, May 26 2016

Keywords

Comments

This is a subsequence of A273756 which considers all odd numbers (2n+1) instead of only prime(n) as coefficients of the linear term.
All terms are necessarily prime, since this is necessary and sufficient to get a prime for x = 0.
The respective minima (= number of consecutive primes for x = 0, 1, 2, ...) are given in A273597.
It has been pointed out by Don Reble that the prime k-tuple conjecture predicts infinitely long sequences of primes of the given form, therefore we consider the "local" maxima, for q below some appropriate (large) limit: see sequences A273756 & A273770 for further details. - M. F. Hasler, Feb 17 2020

Links

Crossrefs

Cf. A273756, A273770.
Cf. also A002837 (n such that n^2-n+41 is prime), A007634 (n such that n^2+n+41 is composite), A005846 (primes of form n^2+n+41), A097823, A144051, A187057 .. A187060, A190800, A191456 ff.

Programs

Formula

a(n) = A273756((prime(n) - 1)/2). - M. F. Hasler, Feb 17 2020

Extensions

Edited and extended using A273756(0..100) due to Don Reble, by M. F. Hasler, Feb 17 2020
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