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

Author

Giovanni Teofilatto, Apr 06 2005

Keywords

• nonn

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Goldbach Conjecture

Crossrefs

Cf. A001172, A000954, first primes in A022885.

Programs

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 *)

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

Extensions

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