A105093 Numbers n such that n = prime(k) + prime(k+3) = prime(k+1) + prime(k+2) for some k.

18, 24, 30, 36, 60, 84, 120, 162, 204, 210, 216, 240, 288, 330, 372, 390, 456, 520, 540, 624, 726, 762, 798, 840, 852, 882, 924, 978, 990, 1104, 1140, 1164, 1200, 1392, 1410, 1428, 1530, 1632, 1650, 1716, 1740, 1764, 1794, 1848, 1974, 2052, 2100, 2112, 2184

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Goldbach Conjecture

Example

a(1)=18 because prime(3)+prime(6)=prime(4)+prime(5)=5+13=7+11=18.

Mathematica

lst = {}; Do[ If[ Prime[n] + Prime[n + 3] == Prime[n + 1] + Prime[n + 2], AppendTo[lst, Prime[n] + Prime[n + 3]]], {n, 184}]; lst (* Robert G. Wilson v, Apr 07 2005 *)

Prog

(Python)
from sympy import nextprime
A105093_list, plist = [], [2, 3, 5, 7]
while len(A105093_list) < 10000:
    m = plist[0]+plist[3]
    if m == plist[1]+plist[2]:
        A105093_list.append(m)
    plist = plist[1:] + [nextprime(plist[-1])] # Chai Wah Wu, Mar 30 2020

Crossrefs

Cf. A001172, A000954, first primes in A022885.

Sequence in context: A160810 A076771 A179014 * A334015 A162331 A092536

Adjacent sequences: A105090 A105091 A105092 * A105094 A105095 A105096

Keyword

nonn

Author

Giovanni Teofilatto, Apr 06 2005

Extensions

Edited and extended by Robert G. Wilson v, Apr 07 2005

Status

approved