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A109981 Primes such that both the sum of digits and the number of digits are primes. 3
11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 137, 139, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 241, 263, 269, 281, 283, 311, 313, 317, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 461, 463, 467, 487, 557, 571, 577, 593 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Cf. A046704 Additive primes: sum of digits is a prime, A088136 Primes such that sum of first and last digits is prime.

LINKS

Reinhard Zumkeller, 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

a(86) = 10037 because both the sum (=11) and number (=5) of digits are primes.

MATHEMATICA

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

PROG

(Haskell)

a109981 n = a109981_list !! (n-1)

a109981_list = filter ((== 1) . a010051' . a055642) a046704_list

-- Reinhard Zumkeller, Nov 16 2012

CROSSREFS

Cf. A046704, A088136.

Cf. A010051, A055642.

Sequence in context: A271983 A136000 A054723 * A091367 A088136 A164932

Adjacent sequences:  A109978 A109979 A109980 * A109982 A109983 A109984

KEYWORD

base,nonn

AUTHOR

Zak Seidov, Jul 06 2005

STATUS

approved

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Last modified December 5 15:24 EST 2016. Contains 278770 sequences.