A109982 Primes p such that index of p, the sum of p's digits and the number of p's digits are all primes.

11, 41, 67, 83, 157, 179, 191, 241, 283, 331, 353, 401, 461, 599, 739, 773, 797, 919, 991, 10079, 10169, 10433, 10457, 10589, 10631, 10723, 10853, 10909, 11311, 11447, 11867, 11953, 12097, 12143, 12301, 12457, 12479, 12503, 12547, 12763, 13003

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(414) = 99551 because its index, 9551, the sum, 29 and number, 5, of digits are all primes.

Mathematica

Select[Prime[Range[200]], PrimeQ[Length[IntegerDigits[ # ]]]&&PrimeQ[Plus@@IntegerDigits[ # ]]&]
Select[Prime[Range[1600]], AllTrue[{PrimePi[#], Total[IntegerDigits[#]], IntegerLength[ #]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 15 2019 *)

Crossrefs

Cf. A046704 Additive primes: sum of digits is a prime, A088136 Primes such that sum of first and last digits is prime, A109981 Primes such that the sum of digits and the number of digits are primes.

Sequence in context: A158205 A179446 A260269 * A128467 A238713 A132232

Adjacent sequences: A109979 A109980 A109981 * A109983 A109984 A109985

Keyword

base,nonn

Author

Zak Seidov, Jul 06 2005

Status

approved