A129633 - OEIS

%I #13 Feb 25 2022 16:24:14

%S 2,3,7,11,13,17,19,31,37,43,83,137,191,197,223,311,347,359,367,389,

%T 449,491,499,503,521,601,647,683,733,751,809,857,881,887,919,953,1019,

%U 1033,1061,1087,1193,1223,1229,1277,1291,1301,1367,1459

%N The sum of the decimal digits of all primes up to and including the primes listed equals a prime.

%C 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 Robert Israel, <a href="/A129633/b129633.txt">Table of n, a(n) for n = 1..10000</a>

%e For 17, 2 + 3 + 5 + 7 + 1+1 + 1+3 + 1+7 = 31, which is prime.

%p S:= 0: R:= NULL: count:= 0: p:= 1:

%p while count < 100 do

%p   p:= nextprime(p);

%p   S:= S + convert(convert(p,base,10),`+`);

%p   if isprime(S) then

%p     count:= count+1; R:= R,p;

%p   fi

%p od:

%p R; # _Robert Israel_, Feb 25 2022

%t 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 nonn,base

%O 1,1

%A _J. M. Bergot_, May 31 2007

%E More terms from _Stefan Steinerberger_, Jun 08 2007