A066875 -id:A066875 - cp's OEIS frontend

A173390 n-th difference between consecutive natural noncomposite numbers = n-th difference between consecutive prime numbers.

1, 3, 16, 37, 40, 47, 55, 56, 74, 103, 108, 111, 119, 130, 161, 165, 185, 188, 195, 200, 219, 240, 272, 273, 292, 340, 359, 388, 420, 427, 465, 466, 509, 521, 554, 600, 606, 622, 630, 634, 668, 683, 684, 703, 710, 711, 734, 762, 792, 814, 822, 823, 830, 831

Offset: 1

Juri-Stepan Gerasimov, Feb 17 2010

nonn

Numbers n such that A075526(n) = A001223(n).

Essentially the same as A066875. - R. J. Mathar, Feb 21 2010

Cf. A001223, A075526.

A075526(a(n)) = A001223(a(n)).

A102552 a(n) = prime(n) - (prime(n+1) + prime(n-1))/2.

Original entry on oeis.org

0, -1, 1, -1, 1, -1, -1, 2, -2, 1, 1, -1, -1, 0, 2, -2, 1, 1, -2, 1, -1, -1, 2, 1, -1, 1, -1, -5, 5, -1, 2, -4, 4, -2, 0, 1, -1, 0, 2, -4, 4, -1, 1, -5, 0, 4, 1, -1, -1, 2, -4, 2, 0, 0, 2, -2, 1, 1, -4, -2, 5, 1, -1, -5, 4, -2, 4, -1, -1, -1, 1, 0, 1, -1, -1, 2, -2, -1, 4, -4, 4, -2, 1, -1, -1, 2, 1, -1, -4, 2, 2, -2, 2, -1, -3, 5, -8, 6, -2, 2, 0, 2, -2

Offset: 3

Yasutoshi Kohmoto, Feb 25 2005

sign

			a(6)=-1 because 13-(17+11)/2=-1.

Eric Weisstein, CRC Concise Encyclopedia of Mathematics, 1998, page 1321.

G. C. Greubel, Table of n, a(n) for n = 3..10000

Cf. A000040, A006562, A036263, A051634, A051635, A066875.

A102552:= func< n | (2*NthPrime(n)-NthPrime(n+1)-NthPrime(n-1))/2 >;
[A102552(n): n in [3..120]]; // G. C. Greubel, Feb 02 2025

a:=n->ithprime(n)-(ithprime(n+1)+ithprime(n-1))/2: seq(a(n),n=3..95); # Emeric Deutsch, Mar 02 2005

f[n_] := Prime[n] - (Prime[n - 1] + Prime[n + 1])/2; Table[f[n], {n, 3, 107}] (* Robert G. Wilson v, Sep 25 2006 *)
#[[2]]-(#[[1]]+#[[3]])/2&/@Partition[Prime[Range[2,110]],3,1] (* Harvey P. Dale, Sep 21 2013 *)

a(n) = prime(n)-(prime(n+1)+prime(n-1))/2;
vector(100,n,a(n+2)) \\ Joerg Arndt, Jan 20 2015

from sympy import sieve as p
def A102552(n): return p[n]-(p[n+1]+p[n-1])//2 # Karl-Heinz Hofmann, May 22 2024

a(n) = (1/2)*(A001223(n) - A001223(n+1)).

a(n) = -A036263(n-1)/2. - T. D. Noe, Oct 06 2006 [corrected by Georg Fischer, Oct 19 2023]

More terms from Emeric Deutsch, Mar 02 2005

cp's OEIS Frontend

A173390 n-th difference between consecutive natural noncomposite numbers = n-th difference between consecutive prime numbers.

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A102552 a(n) = prime(n) - (prime(n+1) + prime(n-1))/2.

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