

A213354


Primes p with digit sums s(p) and s(s(p)) also prime, but s(s(s(p))) not prime.


4



59899999, 69899899, 69899989, 69979999, 69997999, 69999799, 77899999, 78997999, 78998989, 78999889, 78999979, 79699999, 79879999, 79889899, 79979899, 79979989, 79988899, 79989979, 79996999, 79997899, 79997989, 79999789, 79999879, 79999987
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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 kfold digit sum s(s(..s(p)..)) is also prime for all k < n, but not for k = n.
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


LINKS

Table of n, a(n) for n=1..24.


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

Cf. A046704, A070027, A104213, A207293, A207294, A213355, A106807.
Sequence in context: A104329 A104333 A106807 * A186908 A244918 A033624
Adjacent sequences: A213351 A213352 A213353 * A213355 A213356 A213357


KEYWORD

nonn,base


AUTHOR

Jonathan Sondow, Jun 10 2012


STATUS

approved



