A071411 -id:A071411 - cp's OEIS frontend

A024850 Let c(k) denote the k-th composite number and p(k) the k-th prime number; then a(n) = Sum_{i=n(n-1)/2+1 .. n(n+1)/2} c(i) - Sum_{i=1..n} p(i).

2, 9, 21, 46, 84, 135, 206, 308, 429, 583, 772, 987, 1265, 1552, 1906, 2308, 2767, 3278, 3840, 4478, 5201, 5956, 6783, 7704, 8706, 9777, 10976, 12241, 13591, 14985, 16546, 18230, 20019, 21862, 23824, 25907, 28111, 30474, 32897, 35482, 38208, 41125, 44159, 47239, 50516, 53944

Offset: 1

Amarnath Murthy and Benoit Cloitre, Jun 23 2002

nonn

			a(1) = 4 - 2 = 2.
a(2) = 6 + 8 - 2 - 3 = 9.
a(3) = 9 + 10 + 12 - 2 - 3 - 5 = 21.

Cf. A071411.

a(n) = A072475(n) - A007504(n) [corrected by Sean A. Irvine, Jul 26 2019].

a(7) and a(8) corrected and more terms from Sean A. Irvine, Jul 26 2019

A072476 Difference between the sum of first n prime numbers and the sum of first n composite numbers.

Original entry on oeis.org

-2, -5, -8, -10, -9, -8, -5, -1, 6, 17, 28, 44, 63, 82, 104, 131, 163, 196, 233, 272, 312, 357, 405, 458, 517, 579, 642, 707, 772, 840, 921, 1004, 1092, 1181, 1279, 1378, 1481, 1589, 1700, 1816, 1937, 2058, 2187, 2317, 2450, 2584, 2729, 2884, 3042, 3201, 3362, 3527, 3693, 3868, 4048

Offset: 1

Amarnath Murthy, Jun 20 2002

sign

Cf. A071411.

Partial sums of A038529.

Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Table[ Sum[ Prime[i] - Composite[i], {i, 1, n}], {n, 1, 55}]
Module[{nn=60,pr,cm},pr=Prime[Range[nn]];cm=Take[Select[Range[2nn], CompositeQ], nn]; Accumulate[ pr-cm]](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 08 2017 *)

Edited by Robert G. Wilson v, Jun 21 2002

cp's OEIS Frontend

A024850 Let c(k) denote the k-th composite number and p(k) the k-th prime number; then a(n) = Sum_{i=n(n-1)/2+1 .. n(n+1)/2} c(i) - Sum_{i=1..n} p(i).

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A072476 Difference between the sum of first n prime numbers and the sum of first n composite numbers.

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cp's OEIS Frontend

A024850 Let c(k) denote the k-th composite number and p(k) the k-th prime number; then a(n) = Sum_{i=n*(n-1)/2+1 .. n*(n+1)/2} c(i) - Sum_{i=1..n} p(i).

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A072476 Difference between the sum of first n prime numbers and the sum of first n composite numbers.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Extensions

A024850 Let c(k) denote the k-th composite number and p(k) the k-th prime number; then a(n) = Sum_{i=n(n-1)/2+1 .. n(n+1)/2} c(i) - Sum_{i=1..n} p(i).