%I #25 Jul 31 2014 23:47:57

%S 23,31,47,59,695689,698471,883517,992609,992737,993037,1314239,

%T 1324361,1324571,1326511,1327289,1766291,3174029

%N Primes p equal to the sum in base-3 of the digits of all primes < p.

%C Conjecture: this sequence is finite and all terms are shown. - _Robert G. Wilson v_, Jul 27 2014

%C The sum of the digits in base three of all primes < 10^10 is 9694409092. - _Robert G. Wilson v_, Jul 27 2014

%F prime(n) such that, using base 3, prime(n) = sum_{1..n-1} A239619(i).

%e For example, 23 = digit-sum(primes < 23, base=3) = sum(2) + sum(1,0) + sum(1,2) + sum(2,1) + sum(1,0,2) + sum(1,1,1) + sum(1,2,2) + sum(2,0,1).

%t p = 2; s = 0; lst = {}; While[p < 3200000, If[s == p, AppendTo[lst, p]; Print[p]]; s = s + Total@ IntegerDigits[p, 3]; p = NextPrime[p]] (* _Robert G. Wilson v_, Jul 27 2014 *)

%o (PARI) sdt(n) = my(d = digits(n, 3)); sum(i=1, #d, d[i]);

%o lista(nn) = {sp = 0; forprime(p=1, nn, if (p == sp, print1(p, ", ")); sp += sdt(p););} \\ _Michel Marcus_, May 02 2014

%Y Cf. A239619 (Base 3 sum of digits of prime(n)).

%K nonn,base,more

%O 1,1

%A _Anthony Sand_, Apr 14 2014