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.
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 *)
With[{prs=Select[Prime[Range[30]], Mod[#, 6]==5&]}, Select[Union[Rest[ Total/@ Subsets[ prs]]], #<=Max[prs]&]] (* Harvey P. Dale, Mar 11 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Feb 14 2019
STATUS
approved