A051352 a(0) = 0; for n>0, a(n) = a(n-1) + n if n not prime else a(n-1) - n.

0, 1, -1, -4, 0, -5, 1, -6, 2, 11, 21, 10, 22, 9, 23, 38, 54, 37, 55, 36, 56, 77, 99, 76, 100, 125, 151, 178, 206, 177, 207, 176, 208, 241, 275, 310, 346, 309, 347, 386, 426, 385, 427, 384, 428, 473, 519, 472, 520, 569, 619, 670, 722, 669, 723, 778

Offset: 0

Author

Armand Turpel armandt(AT)unforgettable.com

Keywords

• sign
• easy
• nice

Comments

Sequence is not monotonic.

Difference between sum of nonprime numbers and prime numbers <= n. - Zak Seidov, Sep 27 2003

Links

• William A. Tedeschi, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005171, A010051.

Cf. A000217, A034387.

Programs

Haskell

a051352 n = a051352_list !! n
a051352_list = 0 : zipWith (+)
   (a051352_list) (zipWith (*) [1..] $ map ((1 -) . (* 2)) a010051_list)
-- Reinhard Zumkeller, Jan 02 2015

Maple

A034387 := proc(n)
    option remember;
    if n <= 1 then
        0;
    else
        procname(n-1)+ `if`(isprime(n), n, 0)
    end if;
end proc:
A051352 := proc(n)
    n*(n+1)/2 - 2*A034387(n) ;
end proc:
seq(A051352(n),n=0..40) ; # R. J. Mathar, Jun 26 2024

Mathematica

a[0]=0;a[n_]:=a[n]=If[PrimeQ[n],a[n-1]-n,a[n-1]+n]; Table[a[i], {i,0,60}] (* Harvey P. Dale, Apr 07 2011 *)
nxt[{n_,a_}]:={n+1,If[PrimeQ[n+1],a-n-1,a+n+1]}; NestList[nxt,{0,0},60][[All,2]] (* Harvey P. Dale, Sep 07 2022 *)

PARI

a(n) = my(v=primes([1, n])); n*(n+1)/2 -2*vecsum(v); \\ Michel Marcus, Jun 24 2024

Formula

a(n) = a(n-1) + n * (1 - 2*A010051(n)) = a(n-1) + n * (2*A005171(n) - 1) = a(n-1) + n * (A005171(n) - A010051(n)). - Reinhard Zumkeller, Nov 25 2009

a(n) = A000217(n) - 2*A034387(n). - Michel Marcus, Jun 24 2024