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

1,2

Comments

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

Links

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

Formula

PrimePi[A046704(n)]

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A046704.

Cf. A007953, A010051.

Sequence in context: A246397 A015837 A262511 * A062096 A360687 A176008

Adjacent sequences: A075174 A075175 A075176 * A075178 A075179 A075180

Keyword

nonn,base

Author

Zak Seidov, Sep 06 2002

Status

approved