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 A263770 Smallest prime q such that ((prime(n)^2 + q*prime(n))/(prime(n) + 1) is an integer. 2
 7, 5, 7, 17, 13, 29, 19, 41, 73, 31, 97, 191, 43, 89, 97, 109, 61, 311, 137, 73, 149, 241, 337, 181, 197, 103, 313, 109, 331, 229, 257, 397, 139, 281, 151, 457, 317, 821, 337, 349, 181, 547, 193, 389, 199, 401, 1061, 449, 229, 461, 937, 241, 727, 757, 1033, 1321, 271, 1361, 557 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Least prime q such that q == 1 (mod prime(n) + 1). Consists of the initial terms of sequences A002476, A002144, A002476, A007519, A068228, A140444, A061237, A141881, A107008, A132230, A133870, A141868, A124826, A142292, A142398, A141948, A088955, A142003, ... LINKS FORMULA 5 is in this sequence because (prime(2)^2 + 5*prime(2))/(prime(2) + 1) = 6 and 5 is prime. MATHEMATICA Table[q = 2; While[! IntegerQ[(Prime[n]^2 + q Prime@ n)/(Prime@ n + 1)], q = NextPrime@ q]; q, {n, 59}] (* Michael De Vlieger, Oct 26 2015 *) PROG (PARI) a(n) = {p = prime(n); q = 2; while ((p^2 + p*q) % (p + 1), q = nextprime(q+1)); q; } \\ Michel Marcus, Oct 26 2015 CROSSREFS Cf. A263729, A263730, A263769. Sequence in context: A143297 A195348 A072449 * A088839 A111769 A111513 Adjacent sequences:  A263767 A263768 A263769 * A263771 A263772 A263773 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Oct 25 2015 STATUS approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)