

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS

T. D. Noe, Table of n, a(n) for n = 1..4000
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
Adjacent sequences: A224067 A224068 A224069 * A224071 A224072 A224073


KEYWORD

nonn


AUTHOR

G. L. Honaker, Jr., Mar 30 2013


STATUS

approved



