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A036263 Second differences of primes. 23
1, 0, 2, -2, 2, -2, 2, 2, -4, 4, -2, -2, 2, 2, 0, -4, 4, -2, -2, 4, -2, 2, 2, -4, -2, 2, -2, 2, 10, -10, 2, -4, 8, -8, 4, 0, -2, 2, 0, -4, 8, -8, 2, -2, 10, 0, -8, -2, 2, 2, -4, 8, -4, 0, 0, -4, 4, -2, -2, 8, 4, -10, -2, 2, 10, -8, 4, -8, 2, 2, 2, -2, 0, -2, 2, 2, -4, 4, 2, -8, 8, -8, 4, -2, 2, 2, -4, -2, 2, 8, -4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: |a(1)|+|a(2)|+..+|a(n)| ~ prime(n). - Thomas Ordowski, Jul 21 2012

Sum(i=1..n-1, a(i)) = A046933(n), n >= 1. - Daniel Forgues, Apr 15 2014

Sum(i=2..n-1, a(i)) = prime(n+1)-prime(n)-2; Sum(i=2..n-1, a(i))=0 whenever prime(n) is a lesser of twin primes. - Hamdi Murat Yildirim, Jun 24 2014

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

R. G. Batchko, A prime fractal and global quasi-self-similar structure in the distribution of prime-indexed primes, arXiv preprint arXiv:1405.2900, 2014. See Table 2.

FORMULA

a(A064113(n)) = 0. - Reinhard Zumkeller, Jan 20 2012

a(n) = prime(n) + prime(n+2) - 2*prime(n+1). - Thomas Ordowski, Jul 21 2012

a(n) = A001223(n+1) - A001223(n). - R. J. Mathar, Sep 19 2013

EXAMPLE

a(3) = 5 + 11 - 2*7 = 16 - 14 = 2.

MAPLE

A036263:=n->ithprime(n-1) + ithprime(n+1) - 2*ithprime(n); seq(A036263(n), n=2..100); # Wesley Ivan Hurt, Apr 01 2014

MATHEMATICA

Table[Prime[n - 1] + Prime[n + 1] - 2*Prime[n], {n, 2, 105}]

Differences[Prime[Range[100]], 2] (* Harvey P. Dale, Oct 14 2012 *)

PROG

(PARI) for(n=2, 100, print1(prime(n+2)-2*prime(n+1)+prime(n)", "))

(Haskell)

a036263 n = a036263_list !! (n-1)

a036263_list = zipWith (-) (tail a001223_list) a001223_list

-- Reinhard Zumkeller, Oct 29 2011

CROSSREFS

Cf. A001223, A036262, A051635, A006562, A051634, A147812, A147813, A182394, A079054.

Sequence in context: A143526 A072924 A247869 * A168514 A060447 A118177

Adjacent sequences:  A036260 A036261 A036262 * A036264 A036265 A036266

KEYWORD

sign,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 20 04:02 EDT 2014. Contains 248329 sequences.