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%I #21 Feb 04 2021 06:50:38
%S 59899999,69899899,69899989,69979999,69997999,69999799,77899999,
%T 78997999,78998989,78999889,78999979,79699999,79879999,79889899,
%U 79979899,79979989,79988899,79989979,79996999,79997899,79997989,79999789,79999879,79999987
%N Primes p with digit sums s(p) and s(s(p)) also prime, but s(s(s(p))) not prime.
%C 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.
%C Contains primes with digit sums 67, 89, 139, 157, 179,...., A207293(.). So A106807 is a subsequence and examples of numbers in this sequence but not in A106807 are A067180(89), A067180(139) etc. - _R. J. Mathar_, Feb 04 2021
%e 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).
%t 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[#]]]]]]] &]
%Y Cf. A046704, A070027, A104213, A207293, A207294, A213355, A106807.
%K nonn,base
%O 1,1
%A _Jonathan Sondow_, Jun 10 2012
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