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 A105093 Numbers n such that n = prime(k) + prime(k+3) = prime(k+1) + prime(k+2) for some k. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)