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A151960
Sum_{x = A141468(n) to A000040(n)} 1-(-1)^x*x.
0
2, 5, 3, 3, 6, 16, 12, 12, 15, 37, 24, 30, 33, 55, 39, 45, 77, 54, 88, 66, 66, 72, 109, 84, 129, 99, 99, 142, 105, 108, 126, 175, 138, 138, 200, 153, 211, 168, 171, 233, 186, 244, 201, 201, 204, 268, 222, 303, 243, 243, 316, 255, 255, 267, 349, 282
OFFSET
1,1
EXAMPLE
a(1)=1-0+1+1+1-2=2, a(2)=1+1+1-2+1+3=5, a(3)=1-4+1+5=3, a(4)=1-6+1+7=3, a(5)=1-8+1+9+1-10+1+11=6, a(6)=1+9+1-10+1+11+1-12+1+13=16, a(7)=1-10+1+11+1-12+1+13+1-14+1+15+1-16+1+17=12, a(8)=1-12+1+13+1-14+1+15+1-16+1+17+1-18+1+19=12, a(9)=1-14+1+15+1-16+1+17+1-18+1+19+1-20+1+21+1-22+1+23=15, a(10)=1+15+1-16+1+17+1-18+1+19+1-20+1+21+1-22+1+23+1-24+1+25+1-26+1+27+1-28+1+29=37, ...
MATHEMATICA
ZeroAndNonPrime[n_Integer] := FixedPoint[n - 1 + PrimePi@# &, n - 1 + PrimePi@n]; ZeroAndNonPrime[2] = 1; f[n_] := Sum[1-(-1)^x*x, {x, ZeroAndNonPrime@n, Prime@n}]; Array[f, 56]
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Jul 24 2009
Definition clarified by N. J. A. Sloane, Jul 25 2009
Definition corrected by Charles R Greathouse IV, Jul 22 2010
STATUS
approved