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A062020 a(n) = Sum_{i=1..n} Sum_{j=1..i} (prime(i) - prime(j)). 6
0, 1, 6, 17, 44, 81, 142, 217, 324, 485, 666, 913, 1208, 1529, 1906, 2373, 2936, 3533, 4238, 5019, 5840, 6787, 7822, 8995, 10360, 11825, 13342, 14967, 16648, 18445, 20662, 23003, 25536, 28135, 31074, 34083, 37308, 40755, 44354, 48187, 52260 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = a(n-1) + n*prime(n) - Sum_{i = 1..n} prime(i), with a(0) = 0.
a(n) = 2*a(n-1) - a(n-2) + (n-1)*(prime(n) - prime(n-1)), with a(1) = 0, a(2) = 1.
a(n) = Sum_{j=1..n} (2*j - (n+1))*prime(j) = 2*A014285(n) - (n+1)*A007504(n). - G. C. Greubel, May 04 2022
EXAMPLE
a(3) = (5-2) + (5-3) + (3-2) = 6.
MATHEMATICA
a[n_]:= a[n]= If[n<3, (n-1), 2*a[n-1] -a[n-2] +(n-1)*(Prime[n] -Prime[n-1])];
Table[a[n], {n, 50}] (* G. C. Greubel, May 04 2022 *)
PROG
(SageMath)
@CachedFunction
def a(n): # A062020
if (n<3): return (n-1)
else: return 2*a(n-1) - a(n-2) + (n-1)*(nth_prime(n) - nth_prime(n-1))
[a(n) for n in (1..50)] # G. C. Greubel, May 04 2022
CROSSREFS
Sequence in context: A171507 A099858 A232567 * A066183 A262297 A048746
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 02 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jun 05 2001
Name edited by G. C. Greubel, May 04 2022
STATUS
approved

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Last modified February 22 22:43 EST 2024. Contains 370265 sequences. (Running on oeis4.)