A051353 a(n) = a(n-1) + n^2 if n prime else a(n-1) - n, starting with a(0) = 0.

0, -1, 3, 12, 8, 33, 27, 76, 68, 59, 49, 170, 158, 327, 313, 298, 282, 571, 553, 914, 894, 873, 851, 1380, 1356, 1331, 1305, 1278, 1250, 2091, 2061, 3022, 2990, 2957, 2923, 2888, 2852, 4221, 4183, 4144, 4104, 5785, 5743, 7592, 7548, 7503, 7457, 9666, 9618, 9569

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe).

Formula

a(n) = a(n-1) + n*(A010051(n)*(n+1)-1). - Reinhard Zumkeller, Aug 13 2013

Mathematica

nxt[{n_, a_}]:={n+1, If[PrimeQ[n+1], a+(n+1)^2, a-(n+1)]}; Transpose[ NestList[ nxt, {0, 0}, 50]][[2]] (* Harvey P. Dale, Dec 12 2012 *)
FoldList[# + If[PrimeQ[#2], #2^2, -#2] &, Range[0, 50]] (* Paolo Xausa, Dec 27 2025 *)

Prog

(Haskell)
a051353 n = a051353_list !! n
a051353_list = 0 : zipWith (+) a051353_list
   (zipWith (\chi x -> x * (chi * (x + 1) - 1)) a010051_list [1..])
-- Reinhard Zumkeller, Aug 13 2013

Crossrefs

Cf. A010051.

Sequence in context: A337203 A013188 A234947 * A070706 A239932 A114237

Adjacent sequences: A051350 A051351 A051352 * A051354 A051355 A051356

Keyword

sign,easy,nice

Author

Armand Turpel (armandt(AT)unforgettable.com)

Extensions

Name edited by Michel Marcus, Dec 27 2025

Status

approved