A129633 The sum of the decimal digits of all primes up to and including the primes listed equals a prime.

2, 3, 7, 11, 13, 17, 19, 31, 37, 43, 83, 137, 191, 197, 223, 311, 347, 359, 367, 389, 449, 491, 499, 503, 521, 601, 647, 683, 733, 751, 809, 857, 881, 887, 919, 953, 1019, 1033, 1061, 1087, 1193, 1223, 1229, 1277, 1291, 1301, 1367, 1459

Offset

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

S:= 0: R:= NULL: count:= 0: p:= 1:
while count < 100 do
  p:= nextprime(p);
  S:= S + convert(convert(p, base, 10), `+`);
  if isprime(S) then
    count:= count+1; R:= R, p;
  fi
od:
R; # Robert Israel, Feb 25 2022

Mathematica

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 *)

Crossrefs

Sequence in context: A265760 A071200 A038921 * A020622 A045320 A045321

Adjacent sequences: A129630 A129631 A129632 * A129634 A129635 A129636

Keyword

nonn,base

Author

J. M. Bergot, May 31 2007

Extensions

More terms from Stefan Steinerberger, Jun 08 2007

Status

approved