A075177 Indices of additive primes - primes with prime sum-of-digits, see A046704.

1, 2, 3, 4, 5, 9, 10, 13, 14, 15, 18, 19, 23, 24, 26, 30, 32, 33, 34, 36, 37, 40, 41, 43, 44, 45, 46, 48, 49, 50, 53, 56, 57, 60, 61, 64, 65, 66, 67, 68, 71, 72, 74, 75, 78, 79, 80, 82, 86, 87, 89, 90, 91, 93, 102, 105, 106, 108, 109, 110, 111, 116, 117, 118, 121, 124, 128

Offset: 1

Author

Zak Seidov, Sep 06 2002

Keywords

• nonn
• base

Comments

There are 107 additive primes among first 200 primes. There are 38455 additive primes among first 100000 primes. Additive primes are in A046704.

Examples

			Prime(10) = 29 is an additive prime because 2+9 = 11 is prime.
		

Links

• Zak Seidov, Table of n, a(n) for n=1..4086, a(n)<10^4.

Crossrefs

Cf. A046704.

Cf. A007953, A010051.

Programs

Haskell

import Data.List (elemIndices)
a075177 n = a075177_list !! (n-1)
a075177_list = map (+ 1) $
   elemIndices 1 $ map (a010051 . a007953) a000040_list
-- Reinhard Zumkeller, Nov 13 2011

Mathematica

Map[PrimePi[ # ]&, Select[Prime[Range[200]], PrimeQ[Apply[ Plus, IntegerDigits[ # ]]]&]]
Flatten[Position[Prime[Range[150]],?(PrimeQ[Total[IntegerDigits[#]]]&),{1},Heads->False]] (* _Harvey P. Dale, May 29 2013 *)

Formula

a(n) = PrimePi(A046704(n)).

A000040(a(n)) = A046704(n).