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 A324076 Integers which are the sum of distinct primes of the form 6n-1. 2
 5, 11, 16, 17, 22, 23, 28, 29, 33, 34, 39, 40, 41, 45, 46, 47, 51, 52, 53, 56, 57, 58, 59, 62, 63, 64, 68, 69, 70, 71, 74, 75, 76, 80, 81, 82, 83, 85, 86, 87, 88, 89, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A theorem due to Andrzej Makowski: every natural number greater than 161 is the sum of distinct primes of the form "6n-1". (See Sierpiński and David Wells.) All the numbers < 161 and which are the sum of numbers of the form "6n-1" are here in this sequence, complement of A048264. REFERENCES A. Mąkowski, Partitions into unequal primes, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 8 (1960), 125-126. Wacław Sierpiński, Elementary Theory of Numbers, p. 144, Warsaw, 1964. David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Revised edition, 1997, p. 127. LINKS EXAMPLE 22 = 5 + 17; 39 = 5 + 11 + 23; 68 = 5 + 11 + 23 + 29; 139 = 11 + 17 + 23 + 29 + 59. MATHEMATICA Select[Range@ 60, Count[IntegerPartitions[#], _?(And[UnsameQ @@ #, AllTrue[#, And[PrimeQ@ #, Mod[#, 6] == 5] &]] &)] > 0 &] (* Michael De Vlieger, Feb 15 2019 *) CROSSREFS Cf. A002145, A048262 (not the sum of distinct primes of the form 4n-1) Cf. A002144, A048263 (not the sum of distinct primes of the form 4n+1). Cf. A007528, A048264 (not the sum of distinct primes of the form 6n-1). Cf. A002476, A048265 (not the sum of distinct primes of the form 6n+1). Sequence in context: A314080 A337947 A072557 * A314081 A314082 A314083 Adjacent sequences:  A324073 A324074 A324075 * A324077 A324078 A324079 KEYWORD nonn AUTHOR Bernard Schott, Feb 14 2019 STATUS approved

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)