A038377 Number of odd nonprimes <= (2n+1)^2.

1, 2, 5, 11, 20, 32, 47, 66, 85, 110, 137, 167, 200, 237, 276, 320, 365, 414, 467, 522, 579, 643, 708, 777, 845, 924, 997, 1080, 1169, 1255, 1343, 1437, 1536, 1637, 1741, 1847, 1961, 2075, 2187, 2311, 2435, 2560, 2691, 2826, 2962, 3104, 3249, 3393, 3543

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(n) = A037040(n) + 1.

For n>=1, a(n) = 2n^2 + 2n + 2 - PrimePi((2n+1)^2) = A051890(n+1) - A000720((2n+1)^2). - Zak Seidov, Mar 03 2008

Example

a(2) = 5 because there are 5 odd nonprimes that are not exceeding (2*2+1)^2 = 25: 1, 9, 15, 21 and 25.

Mathematica

nn=20001; With[{onps=Complement[Range[1, nn, 2], Prime[Range[PrimePi[nn+1]]]]}, Table[Count[onps, _?(#<=(2n+1)^2&)], {n, 0, 60}]]  (* Harvey P. Dale, Apr 13 2011 *)
a[n_] := 2*n^2 + 2*n + 2 - PrimePi[(2*n + 1)^2]; a[0] = 1; Array[a, 61, 0] (* Amiram Eldar, Sep 06 2024 *)

Prog

(PARI) a(n) = if(n == 0, 1, 2*n^2 + 2*n + 2 - primepi((2*n + 1)^2)); \\ Amiram Eldar, Sep 06 2024

Crossrefs

Cf. A000720, A037040, A051890.

Sequence in context: A179632 A093871 A139482 * A261227 A022908 A256310

Adjacent sequences: A038374 A038375 A038376 * A038378 A038379 A038380

Keyword

nonn

Author

N. J. A. Sloane and Erich Friedman

Extensions

Offset corrected by Amiram Eldar, Sep 06 2024

Status

approved