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%I A129633 #13 Feb 25 2022 16:24:14
%S A129633 2,3,7,11,13,17,19,31,37,43,83,137,191,197,223,311,347,359,367,389,
%T A129633 449,491,499,503,521,601,647,683,733,751,809,857,881,887,919,953,1019,
%U A129633 1033,1061,1087,1193,1223,1229,1277,1291,1301,1367,1459
%N A129633 The sum of the decimal digits of all primes up to and including the primes listed equals a prime.
%C A129633 Up to 50000 there are only five groups of twins: (11,13) - (17,19) - (2141,2143) - (3939,3931) - (48677,48679). - _Carmine Suriano_, Jul 22 2010, corrected by _Robert Israel_, Feb 25 2022
%H A129633 Robert Israel, <a href="/A129633/b129633.txt">Table of n, a(n) for n = 1..10000</a>
%e A129633 For 17, 2 + 3 + 5 + 7 + 1+1 + 1+3 + 1+7 = 31, which is prime.
%p A129633 S:= 0: R:= NULL: count:= 0: p:= 1:
%p A129633 while count < 100 do
%p A129633   p:= nextprime(p);
%p A129633   S:= S + convert(convert(p,base,10),`+`);
%p A129633   if isprime(S) then
%p A129633     count:= count+1; R:= R,p;
%p A129633   fi
%p A129633 od:
%p A129633 R; # _Robert Israel_, Feb 25 2022
%t A129633 a = {}; su = 0; For[n = 1, n < 300, n++, su = su + Plus@@IntegerDigits[Prime[n]]; If[PrimeQ[su], AppendTo[a, Prime[n]]]]; a (* _Stefan Steinerberger_, Jun 08 2007 *)
%K A129633 nonn,base
%O A129633 1,1
%A A129633 _J. M. Bergot_, May 31 2007
%E A129633 More terms from _Stefan Steinerberger_, Jun 08 2007

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