A240886 Primes p equal to the sum in base-3 of the digits of all primes < p.

23, 31, 47, 59, 695689, 698471, 883517, 992609, 992737, 993037, 1314239, 1324361, 1324571, 1326511, 1327289, 1766291, 3174029

Offset: 1

Author

Anthony Sand, Apr 14 2014

Keywords

• nonn
• base
• more

Comments

Conjecture: this sequence is finite and all terms are shown. - Robert G. Wilson v, Jul 27 2014

The sum of the digits in base three of all primes < 10^10 is 9694409092. - Robert G. Wilson v, Jul 27 2014

Examples

			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).
		

Crossrefs

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

Programs

Mathematica

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 *)

PARI

sdt(n) = my(d = digits(n, 3)); sum(i=1, #d, d[i]);
lista(nn) = {sp = 0; forprime(p=1, nn, if (p == sp, print1(p, ", ")); sp += sdt(p););} \\ Michel Marcus, May 02 2014

Formula

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