The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (Python) from sympy import isprime, primerange def nontwins(N):     return [p for p in primerange(1, N+1) if not (isprime(p-2) or isprime(p+2))] def auptont(N): # all terms where the larger non-twin <= N     nt = nontwins(N)     return [sum((-1)**(j+1)*j for j in range(nt[i], nt[i+1]+1)) for i in range(len(nt)-1)] print(auptont(565)) # Michael S. Branicky, Nov 30 2021 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 30 14:51 EDT 2022. Contains 354943 sequences. (Running on oeis4.)