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 A087037 Smallest integer x > 0 such that x^x + n is prime, or 0 if no such x exists. 4
 1, 1, 2, 1, 444, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sequence with the unknown terms a(8), a(11), a(17), a(24), a(41), a(53), a(59), a(65) indicated by ? (each of which exceeds 6000) begins: 1, 1, 2, 1, 444, 1, 2, ?, 2, 1, ?, 1, 2, 3, 2, 1, ?, 1, 2, 3, 4, 1, 6, ?, 2, 3, 2, 1, 30, 1, 6, 3, 2, 3, 6, 1, 2, 5, 2, 1, ?, 1, 2, 3, 58, 1, 6, 7, 2, 3017, 4, 1, ?, 35, 2, 3, 2, 1, ?, 1, 4, 3, 2, 19, ?, 1, 2, 27, 2, 1, 6, 1, 8, 3, 2, ..., where the value a(50)=3017 corresponds to a probable prime. [extended by Jon E. Schoenfield, Mar 17 2018, Mar 19 2018] It is conjectured that such x always exists. - Dean Hickerson From Farideh Firoozbakht and M. F. Hasler, Nov 27 2009: (Start) We can show that for all n=(6k-1)^3, k > 0, there is no such x, which disproves the conjecture: Since n=(6k-1)^3 is odd, x must be even, else x^x+n is even and composite. If x == +-1 (mod 3), then x^x + n == (+-1)^2 + (-1)^3 == 0 (mod 3), i.e., divisible by 3 and therefore composite. Finally, if x == 0 (mod 3), then x^x + n = (x^(x/3) + 6k-1)*(x^(2x/3) - x^(x/3)*(6k-1) + (6k-1)^2) is again composite. (End) a(8) >= 36869. - Max Alekseyev, Sep 16 2013 LINKS OpenPFGW Project, Primality Tester EXAMPLE a(7)=2 because 2^2 + 7 = 11 is prime. PROG (PARI) a(n) = {my(x = 1); while (!isprime(x^x+n), x++); x; } \\ Michel Marcus, Mar 20 2018 CROSSREFS Cf. A000312 (n^n), A087038 (x^x+n is prime, x>1). Cf. A166853 (x^x-n is prime). - Farideh Firoozbakht and M. F. Hasler, Nov 27 2009 Sequence in context: A012867 A178393 A272538 * A036109 A240234 A098940 Adjacent sequences:  A087034 A087035 A087036 * A087038 A087039 A087040 KEYWORD nonn,more,hard AUTHOR Hugo Pfoertner, Jul 31 2003 EXTENSIONS Name edited by Altug Alkan, Apr 01 2018 STATUS approved

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)