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A105093
Numbers n such that n = prime(k) + prime(k+3) = prime(k+1) + prime(k+2) for some k.
4
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
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: A076771 A375162 A179014 * A334015 A162331 A092536
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, Apr 06 2005
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 07 2005
STATUS
approved