The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 * A354913 A036109 A240234 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)