OFFSET

1,1

COMMENTS

A046704 is primes p with s(p) also prime. A207294 is primes p with s(p) and s(s(p)) also prime. A070027 is primes p with all s(p), s(s(p)), s(s(s(p))), ... also prime. A104213 is primes p with s(p) not prime. A207293 is primes p with s(p) also prime, but not s(s(p)). A213355 is smallest prime p whose k-fold digit sum s(s(..s(p)..)) is also prime for all k < n, but not for k = n.

EXAMPLE

59899999 and s(59899999) = 5+9+8+9+9+9+9+9 = 67 and s(s(59899999)) = s(67) = 6+7 = 13 are all primes, but s(s(s(59899999))) = s(13) = 1+3 = 4 is not prime. No smaller prime has this property, so a(1) = 59899999 = A213355(3).

MATHEMATICA

Select[Prime[Range[5000000]], PrimeQ[Apply[Plus, IntegerDigits[#]]] && PrimeQ[Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[#]]]]] && ! PrimeQ[Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[#]]]]]]] &]

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Jonathan Sondow, Jun 10 2012

STATUS

approved