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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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified April 17 08:40 EDT 2021. Contains 343064 sequences. (Running on oeis4.)