A054265 Sum of composite numbers between successive primes.

0, 4, 6, 27, 12, 45, 18, 63, 130, 30, 170, 117, 42, 135, 250, 280, 60, 320, 207, 72, 380, 243, 430, 651, 297, 102, 315, 108, 333, 1560, 387, 670, 138, 1296, 150, 770, 800, 495, 850, 880, 180, 1674, 192, 585, 198, 2255, 2387, 675, 228, 693, 1180, 240, 2214, 1270

Offset

1,2

Links

James Spahlinger, Table of n, a(n) for n = 1..1000

Paul Barry, On the Gap-sum and Gap-product Sequences of Integer Sequences, arXiv:2104.05593 [math.CO], 2021.

Formula

a(n) = (prime(n+1) + prime(n))*(prime(n+1) - prime(n) - 1)/2. - Zak Seidov, Sep 12 2002

Example

Between 7 and 11 we have 8 + 9 + 10 which is a(4)=27.

Prog

(PARI) a(n) = (prime(n+1) + prime(n))*(prime(n+1) - prime(n) - 1)/2; \\ Michel Marcus, Mar 24 2016
(Python)
from sympy import nextprime, prime
def A054265(n): return ((p:=prime(n))+(q:=nextprime(p)))*(q-p-1)>>1 # Chai Wah Wu, Jun 01 2024

Crossrefs

Cf. A000040, A046933, A054264, A054266, A054267, A054268.

Sequence in context: A193689 A099941 A074120 * A105409 A109934 A068321

Adjacent sequences: A054262 A054263 A054264 * A054266 A054267 A054268

Keyword

nonn

Author

Patrick De Geest, Apr 15 2000

Status

approved