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 A167770 a(n) = prime(n)^2 modulo prime(n+1). 6
 1, 4, 4, 5, 4, 16, 4, 16, 7, 4, 36, 16, 4, 16, 36, 36, 4, 36, 16, 4, 36, 16, 36, 64, 16, 4, 16, 4, 16, 69, 16, 36, 4, 100, 4, 36, 36, 16, 36, 36, 4, 100, 4, 16, 4, 144, 144, 16, 4, 16, 36, 4, 100, 36, 36, 36, 4, 36, 16, 4, 100, 196, 16, 4, 16, 196, 36, 100, 4, 16, 36, 64, 36, 36, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Only for three cases n = 4,9,30, a(n) < (prime(n+1)-prime(n))^2 because only in these cases(prime(n+1)-prime(n))^2 > prime(n+1): n = 4: a(4) = 5 < ((p(5)-p(4))^2 = (11-7)^2 = 16) and 16 > 11. n = 9: a(9) = 7 < ((p(10)-p(9))^2 = (29-23)^2 = 36) and 36 > 29. n = 30: a(30) = 69 < ((p(31)-p(30))^2 = (127-113)^2 = 196) and 196 > 127. In all other cases, a(n) = A076821(n) = (prime(n+1)-prime(n))^2, is highly probable but not proved conjecture. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA a(n) = prime(n)^2 modulo prime(n+1). a(n) == A001223(n)^2 (mod A000040(n+1)). - L. Edson Jeffery, Oct 01 2014 MAPLE A167770:=n->ithprime(n)^2 mod ithprime(n+1): seq(A167770(n), n=1..70); # Wesley Ivan Hurt, Oct 01 2014 MATHEMATICA Table[PowerMod[Prime[n], 2, Prime[n+1]], {n, 221265}] PROG (PARI) a(n)=prime(n)^2%prime(n+1) \\ M. F. Hasler, Oct 04 2014 CROSSREFS Cf. A076821 (squares of the differences between consecutive primes). Cf. A001223 (modular square roots of this sequence). Cf. A000040 (primes), A001248 (squares of primes). Sequence in context: A226446 A158086 A195783 * A080800 A253443 A140341 Adjacent sequences:  A167767 A167768 A167769 * A167771 A167772 A167773 KEYWORD nonn AUTHOR Zak Seidov, Nov 11 2009 STATUS approved

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Last modified September 16 10:46 EDT 2019. Contains 327094 sequences. (Running on oeis4.)