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%I #20 Apr 16 2018 19:21:15
%S 2,11,101,3,13,31,103,211,1021,1201,2011,3001,10111,20011,20101,21001,
%T 100003,102001,1000003,1011001,1020001,1100101,2100001,10010101,
%U 10100011,20001001,30000001,101001001,200001001,1000000021,1000001011
%N Primes sorted on digit sums, then on the primes.
%C Beyond n = 4, a(n) is believed to coincide with A062339.
%C Only correct for n >= 4 if an undiscovered prime of digit sum two (which would have to be a member of A080176) does not exist; this is conjectured but not proved. - _Jeppe Stig Nielsen_, Mar 30 2018
%e There are only three primes with a digit sum of 2, and those are 2, 11, 101. Therefore these three primes are the first three terms of this sequence.
%e There is only one prime with a digit sum of 3, and that's 3 itself. Any higher number with a digit sum of 3 is a nontrivial multiple of 3 and therefore composite.
%e Then follows the first prime with a digit sum of 4, which is 13.
%t Prime@ Flatten@ Values@ Take[KeySort@ PositionIndex[Total@ IntegerDigits@ # & /@ Prime@ Range[10^7]], 3] (* _Michael De Vlieger_, Apr 07 2018 *)
%Y Cf. A062341.
%K nonn,base
%O 1,1
%A _Lekraj Beedassy_, Mar 04 2009
%E Comment edited by _Robert Israel_, Dec 28 2015