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%I #56 Dec 17 2021 20:28:31
%S 2,3,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35,37,
%T 38,40,41,43,44,46,47,49,50,52,53,55,56,58,59,61,62,64,65,67,68,70,71,
%U 73,74,76,77,79,80,82,83,85,86,88,89,91,92,94,95,97,98,100,101,103
%N Sum of digits of primes (A007605), sorted and with duplicates removed.
%C Presumably this is 3 together with numbers greater than 1 and not divisible by 3 (see A001651). - _Charles R Greathouse IV_, Jul 17 2013. (This is not a theorem because we do not know if, given s > 3 and not a multiple of 3, there is always a prime with digit-sum s. Cf. A067180, A067523. - _N. J. A. Sloane_, Nov 02 2018)
%C From _Chai Wah Wu_, Nov 04 2018: (Start)
%C Conjecture: for s > 10 and not a multiple of 3, there exists a prime with digit-sum s consisting only of the digits 2 and 3 (cf. A137269). This conjecture has been verified for s <= 2995.
%C Conjecture: for s > 18 and not a multiple of 3, there exists a prime with digit-sum s consisting only of the digits 3 and 4. This conjecture has been verified for s <= 1345.
%C Conjecture: for s > 90 and not a multiple of 3, there exists a prime with digit-sum s consisting only of the digits 8 and 9. This conjecture has been verified for s <= 8995.
%C Conjecture: for 0 < a < b < 10, gcd(a, b) = 1 and ab not a multiple of 10, if s > 90 and s is not a multiple of 3, then there exists a prime with digit-sum s consisting only of the digits a and b. (End)
%H Chai Wah Wu, <a href="/A133223/b133223.txt">Table of n, a(n) for n = 1..5997</a>
%Y Cf. A007605, A067523, A067180, A106754-A106787, A062339, A062341, A062337, A137269.
%K nonn,base
%O 1,1
%A _Lekraj Beedassy_, Dec 19 2007
%E Corrected by _Jeremy Gardiner_, Feb 09 2014