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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.
4
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
2,1
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
FORMULA
a(n) = A273756((prime(n) - 1)/2). - M. F. Hasler, Feb 17 2020
PROG
(PARI) A273595(n)=A273756(prime(n)\2) \\ changed Feb 17 2020
CROSSREFS
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.
Sequence in context: A140755 A095479 A156783 * A334094 A033230 A330981
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 26 2016
EXTENSIONS
Edited and extended using A273756(0..100) due to Don Reble, by M. F. Hasler, Feb 17 2020
STATUS
approved