A094914 Absolute value of n^2 + n - 1354363.

1354361, 1354357, 1354351, 1354343, 1354333, 1354321, 1354307, 1354291, 1354273, 1354253, 1354231, 1354207, 1354181, 1354153, 1354123, 1354091, 1354057, 1354021, 1353983, 1353943, 1353901, 1353857, 1353811, 1353763, 1353713, 1353661, 1353607, 1353551, 1353493

Offset

1,1

Comments

a(n) generates primes with probability >1/2 for a random integer [1,10^4] (see reference). For confirmation, I checked the distribution of primes using the link. Results up to a(24) are shown below. P and C stand for prime and composite, respectively. a(1):P a(2):C a(3):C a(4):P a(5):P a(6):P a(7):P a(8):P a(9):C a(10):C a(11):P a(12):P a(13):P a(14):P a(15):C a(16):C a(17):P a(18):P a(19):P a(20):C a(21):P a(22):P a(23):C a(24):P Probability was 16/24 > 1/2.

Primes in this sequence are in A120609. - Elmo R. Oliveira, Apr 21 2026

References

Richard Crandall and Carl Pomerance, "Prime numbers: a computational perspective", Springer-Verlag, Inc., NY, 2001, p. 49.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..2000

Chris Caldwell, Prime test.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = abs(n^2 + n - 1354363).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for 4 <= n <= 1163 and n >= 1167. - Jason Yuen, Apr 22 2026

Mathematica

A094914[n_] := Abs[n^2 + n - 1354363]; Array[A094914, 30] (* Paolo Xausa, May 02 2026 *)

Prog

(PARI) a(n)=abs(n^2+n-1354363) \\ Charles R Greathouse IV, Oct 16 2012

Crossrefs

Cf. A120609 (primes).

Sequence in context: A184661 A187961 A120609 * A138027 A222155 A250502

Adjacent sequences: A094911 A094912 A094913 * A094915 A094916 A094917

Keyword

nonn,easy

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jun 18 2004

Status

approved