A133450 Difference between 4*n^2 and the average of the two prime numbers which bracket this number.

0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 1, 2, 1, 4, 3, -2, -2, 2, 1, 1, -4, -5, -5, 1, 10, 1, 3, 7, -2, 0, 4, 0, 3, -5, 4, 0, 2, 12, 0, -9, -2, 6, -6, -3, 3, 0, 2, 1, -3, 10, -9, 1, 10, -3, 1, 0, 4, 2, -2, 5, 1, 1, 8, -12, 5, -1, 8, -2, 0, 0, -3, -1, 1, 2, 8, -4, 12, 3, 4, 5, 1, -2, -10, 0, 10

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A056929(2n). - M. F. Hasler, Dec 26 2007

Example

a(1)=0 because 4 - (3 + 5)/2 = 0
a(2)=1 because 16 - (13 + 17)/2 = 1
a(3)=2 because 36 - (31 + 37)/2 = 2
a(4)=0 because 64 - (61 + 67)/2 = 0
a(5)=1 because 100 - (97 + 101)/2 = 1

Mathematica

Table[n^2-(Prime[PrimePi[n^2]]+Prime[PrimePi[n^2]+1])/2, {n, 2, 200, 2}] (* Zak Seidov *)
diff4[n_]:=Module[{x=4n^2}, x-(NextPrime[x]+NextPrime[x, -1])/2]; Array[ diff4, 90] (* Harvey P. Dale, Aug 31 2017 *)

Prog

(PARI) A133450(n)=4*n^2-(precprime(4*n^2)+nextprime(4*n^2))/2 \\ M. F. Hasler, Dec 26 2007

Crossrefs

Cf. A056929, A101593, A075190.

Sequence in context: A119346 A014586 A122924 * A029410 A242082 A159917

Adjacent sequences: A133447 A133448 A133449 * A133451 A133452 A133453

Keyword

sign

Author

Alexander R. Povolotsky, Dec 22 2007

Extensions

Corrected and extended by Zak Seidov, Dec 23 2007

Edited by N. J. A. Sloane, Dec 23 2007

Status

approved