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A162734 An alternating sum of all numbers from the n-th up to the (n+1)st isolated prime. 3
11, 30, 42, 50, 60, 73, 81, 86, 93, 105, 120, 129, 144, 160, 165, 170, 192, 217, 228, 242, 254, 260, 270, 285, 300, 312, 324, 334, 345, 356, 363, 370, 376, 381, 386, 393, 399, 405, 424, 441, 446, 453, 462, 473, 483, 489, 495, 501, 506, 525, 544, 552, 560 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

11 followed by the average of each two consecutive non-twin primes. - Colin Barker, Jul 17 2014

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = sum_{j= A007510(n).. A007510(n+1)} (-1)^(j+1)*j = A001057(A007510(n+1))-A001057(A007510(n)-1).

EXAMPLE

a(1) = -2+3-4+5-6+7-8+9-10+11-12+13-14+15-16+17-18+19-20+21-22+23 = 11.

a(2) = 23-24+25-26+27-28+29-30+31-32+33-34+35-36+37 = 30.

MAPLE

N:= 1000: # to get all terms where the larger non-twin <= N

Primes:= select(isprime, {seq(2*i-1, i=1..floor((N+1)/2))}):

NonTwins:= Primes minus (map(t->t+2, Primes) union map(t->t-2, Primes)):

11, seq((NonTwins[i]+NonTwins[i+1])/2, i=1..nops(NonTwins)-1); # Robert Israel, Jul 21 2014

PROG

(PARI)

non_twin_primes(pmax) = my(s=[]); forprime(p=2, pmax, if(!isprime(p-2) && !isprime(p+2), s=concat(s, p))); s

a162734(maxp) = my(ntp=non_twin_primes(maxp)); vector(#ntp-1, n, sum(k=ntp[n], ntp[n+1], -k*(-1)^k))

a162734(500) \\ Colin Barker, Jul 17 2014

CROSSREFS

Cf. A007510.

Sequence in context: A271348 A057739 A146751 * A163060 A247433 A051682

Adjacent sequences:  A162731 A162732 A162733 * A162735 A162736 A162737

KEYWORD

nonn,less

AUTHOR

Juri-Stepan Gerasimov, Jul 13 2009

EXTENSIONS

Replaced 55 by 60 and 447 by 446 - R. J. Mathar, Sep 23 2009

STATUS

approved

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Last modified April 23 04:23 EDT 2021. Contains 343199 sequences. (Running on oeis4.)