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A224070
Sets of four primes such that the sum of any three is prime, ordered first by sum, then lexicographically.
1
5, 7, 17, 19, 7, 11, 13, 23, 7, 13, 17, 23, 5, 13, 19, 29, 5, 11, 13, 43, 11, 13, 19, 29, 5, 7, 19, 47, 5, 17, 19, 37, 7, 11, 19, 41, 11, 17, 19, 31, 5, 11, 31, 37, 5, 13, 23, 43, 11, 13, 17, 43, 11, 13, 23, 37, 13, 17, 23, 31, 7, 11, 19, 53, 7, 11, 29, 43
OFFSET
1,1
LINKS
Chris Caldwell and G. L. Honaker, Jr., Prime Curios!
EXAMPLE
The first four terms of the sequence are 5, 7, 17, 19. The sum of any three is prime: 5 + 7 + 17 = 29, 5 + 7 + 19 = 31, 5 + 17 + 19 = 41, 7 + 17 + 19 = 43. This set of four primes has the smallest possible sum, 48, and is unique.
There are two such sets of four primes with sum 72: {5, 11, 13, 43} and {11, 13, 19, 29}. The first set is listed first since it is lexicographically earliest.
MATHEMATICA
MaxSum = 100; nn = PrimePi[MaxSum - 15]; ps = {}; Do[p = Prime[{a, b, c, d}]; If[Total[p] <= MaxSum, AppendTo[ps, p]], {a, 2, nn - 3}, {b, a + 1, nn - 2}, {c, b + 1, nn - 1}, {d, c + 1, nn}]; s = Select[ps, And @@ PrimeQ /@ (Total[#] - #) &]; s2 = SortBy[s, Total]; Flatten[s2] (* T. D. Noe, Apr 01 2013 *)
CROSSREFS
Cf. A000040.
Sequence in context: A341038 A070372 A082818 * A075089 A075305 A140564
KEYWORD
nonn
AUTHOR
G. L. Honaker, Jr., Mar 30 2013
STATUS
approved