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A273595
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Least q > 0 such that min { x >= 0 | q + prime(n)*x + x^2 is composite } is a (local) maximum, cf. A273756 & A273770.
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4
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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
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OFFSET
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2,1
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COMMENTS
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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
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LINKS
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FORMULA
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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