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 A257231 a(n) = n^2 mod p where p is the least prime greater than n. 2
 1, 1, 4, 1, 4, 1, 5, 9, 4, 1, 4, 1, 16, 9, 4, 1, 4, 1, 16, 9, 4, 1, 7, 25, 16, 9, 4, 1, 4, 1, 36, 25, 16, 9, 4, 1, 16, 9, 4, 1, 4, 1, 16, 9, 4, 1, 36, 25, 16, 9, 4, 1, 36, 25, 16, 9, 4, 1, 4, 1, 36, 25, 16, 9, 4, 1, 16, 9, 4, 1, 4, 1, 36, 25, 16, 9, 4, 1, 16, 9, 4, 1, 36, 25, 16, 9, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: a(n) is always a positive square, except for the terms 5, 7, 69, 42 and 17 given by n = 7, 23, 113, 114, and 115 respectively. It is easy to show that nonsquare terms are in [p, q) iff p and q are consecutive primes and q-p > sqrt(q). There are no gaps between consecutive primes greater than sqrt(q) for 127 < q < 4*10^18 (see Nicely's table of maximal prime gaps). LINKS Chris Boyd, Table of n, a(n) for n = 1..10000 Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101] Tomás Oliveira e Silva, Gaps between consecutive primes EXAMPLE a(23) = 7 because 23^2 mod 29 = 7. a(24) = 25 because 24^2 mod 29 = 25. MATHEMATICA Table[Mod[n^2, NextPrime@ n], {n, 87}] (* Michael De Vlieger, Apr 19 2015 *) Table[PowerMod[n, 2, NextPrime[n]], {n, 90}] (* Harvey P. Dale, May 24 2015 *) PROG (PARI) a(n)=n^2%nextprime(n+1) (Magma) [n^2 mod NextPrime(n): n in [1..80]]; // Vincenzo Librandi, Apr 19 2015 CROSSREFS Cf. A257230. Sequence in context: A074393 A267633 A095666 * A196757 A193254 A193454 Adjacent sequences: A257228 A257229 A257230 * A257232 A257233 A257234 KEYWORD nonn,easy AUTHOR Chris Boyd, Apr 19 2015 STATUS approved

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Last modified August 14 19:51 EDT 2024. Contains 375167 sequences. (Running on oeis4.)