A286901 Sum of the numbers from prevprime(n) to n.

5, 7, 12, 11, 18, 15, 24, 34, 45, 23, 36, 27, 42, 58, 75, 35, 54, 39, 60, 82, 105, 47, 72, 98, 125, 153, 182, 59, 90, 63, 96, 130, 165, 201, 238, 75, 114, 154, 195, 83, 126, 87, 132, 178, 225, 95, 144, 194, 245, 297, 350, 107, 162, 218, 275, 333, 392, 119, 180, 123

Offset

3,1

Comments

n is the lesser of twin primes (A001359) iff a(n+2) = A286900(n).

Links

Chai Wah Wu, Table of n, a(n) for n = 3..10000

Formula

a(n) = Sum_{i=prevprime(n)..n} i.

Maple

A286901:=n->add(i, i=prevprime(n)..n): seq(A286901(n), n=3..100);

Mathematica

Array[Total@ Range[NextPrime[#, -1], #] &, 60, 3] (* Michael De Vlieger, May 15 2017 *)

Prog

(Python)
from __future__ import division
from sympy import prevprime
def A286901(n):
    m = prevprime(n)
    return (m + n)*(n - m + 1)//2 # Chai Wah Wu, Feb 26 2018

Crossrefs

Cf. A001359, A286900 (sum of the numbers from n to nextprime(n)).

Sequence in context: A333436 A086255 A306513 * A171490 A047382 A314301

Adjacent sequences: A286898 A286899 A286900 * A286902 A286903 A286904

Keyword

nonn,easy,look

Author

Wesley Ivan Hurt, May 15 2017

Extensions

a(25) inserted by Chai Wah Wu, Feb 26 2018

Status

approved