A167770 - OEIS

A167770

a(n) = prime(n)^2 modulo prime(n+1).

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

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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: A195783 A376178 A360997 * A080800 A253443 A140341

Adjacent sequences: A167767 A167768 A167769 * A167771 A167772 A167773

KEYWORD

nonn

AUTHOR

Zak Seidov, Nov 11 2009

STATUS

approved