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A207294 Primes p whose digit sum s(p) and iterated digit sum s(s(p)) are also prime. 5
2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 83, 101, 113, 131, 137, 151, 173, 191, 223, 227, 241, 263, 281, 311, 313, 317, 331, 353, 401, 421, 443, 461, 599, 601, 641, 797, 821, 887, 911, 977, 1013, 1019, 1031, 1033, 1051, 1091, 1103, 1109, 1123, 1163, 1181, 1213, 1217 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum_{a(n) < x} 1/a(n) is asymptotic to (9/4)*log(log(log(log(x)))) as x -> infinity; see Harman (2012). Thus the sequence is infinite.

The first member not in A070027 is 59899999.

A046704 is primes p with 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)). A213354 is primes p with s(p) and s(s(p)) also prime, but not s(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.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

G. Harman, Counting Primes whose Sum of Digits is Prime, J. Integer Seq., 15 (2012), Article 12.2.2.

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, so 59899999 is a member. But s(s(s(59899999))) = s(13) = 1+3 = 4 is not prime, so 59899999 is not a member of A070027.

MATHEMATICA

Select[Prime[Range[200]], PrimeQ[Apply[Plus, IntegerDigits[#]]] && PrimeQ[Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[#]]]]] &]

PROG

(PARI) select(p->my(s=sumdigits(p)); isprime(s)&&isprime(sumdigits(s)), primes(1000)) \\ Charles R Greathouse IV, Jun 10 2012

CROSSREFS

Cf. A046704, A070027, A104213, A207293, A213354, A213355.

Sequence in context: A089392 A089695 A070027 * A156658 A118723 A118721

Adjacent sequences:  A207291 A207292 A207293 * A207295 A207296 A207297

KEYWORD

nonn,base

AUTHOR

Jonathan Sondow, Jun 09 2012

STATUS

approved

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Last modified October 17 12:56 EDT 2019. Contains 328112 sequences. (Running on oeis4.)