A075544 Primes which are the sum of the digital root of the first n primes for some n.

2, 5, 17, 19, 23, 31, 37, 43, 71, 163, 179, 199, 263, 269, 347, 379, 389, 443, 467, 487, 499, 569, 601, 641, 643, 647, 683, 691, 709, 769, 821, 829, 857, 859, 919, 941, 947, 953, 967, 997, 1019, 1021, 1061, 1093, 1123, 1153, 1231, 1249, 1381, 1409, 1459

Offset: 1

Author

Jon Perry, Oct 11 2002

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A010888, A104247.

Programs

Mathematica

s = 0; Do[s = s + Mod[ Prime[n], 9]; If[ PrimeQ[s], Print[s]], {n, 1, 350} ]
Select[Accumulate[Mod[Prime[Range[1000]],9]],PrimeQ] (* Harvey P. Dale, May 04 2012 *)

PARI

sumdigits2(n)=local(c); while (n>9,c=0; while (n>0,c=c+n%10; n=n-n%10; n=n/10); n=c); n
c=0; forprime (p=2,1000,c=c+sumdigits2(p); if (isprime(c),print1(c,",")))

Extensions

Edited by Robert G. Wilson v, Oct 14 2002

Definition corrected by M. F. Hasler, Apr 04 2007

Corrected by Harvey P. Dale, May 04 2012