A127355 Primes with prime digit counts. The digit count numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number.

3, 7, 17, 23, 71, 101, 103, 107, 109, 113, 127, 131, 137, 173, 199, 223, 233, 271, 311, 313, 317, 331, 359, 367, 409, 479, 499, 593, 673, 677, 701, 709, 773, 797, 907, 919, 929, 947, 953, 977, 991, 1009, 1123, 1129, 1193, 1213, 1217, 1223, 1231, 1277, 1291

Offset

1,1

Comments

Compare with "Look And Say" version A056815.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A010051(a(n)) * A010051(A047842(a(n))) = 1. - Reinhard Zumkeller, Apr 14 2014

Example

The primes 479,991,1747 respectively have digit counts 141719 (one 4,one 7,one 9), 1129 (one 1, two 9's), 111427 (one 1, one 4, two 7's) which are also prime; So they belong to the sequence.

Mathematica

dc[n_] :=FromDigits@Flatten@Select[Table[{DigitCount[n, 10, k], k}, {k, 0, 9}], #[[1]] > 0 &]; Select[Prime@Range[210], PrimeQ[dc[ # ]] &] (* Ray Chandler, Jan 16 2007 *)

Prog

(Haskell)
a127355 n = a127355_list !! (n-1)
a127355_list = filter ((== 1) . a010051' . a047842) a000040_list
-- Reinhard Zumkeller, Apr 14 2014

Crossrefs

Cf. A047842, A127354.

Sequence in context: A118940 A127175 A339943 * A079470 A056815 A127176

Adjacent sequences: A127352 A127353 A127354 * A127356 A127357 A127358

Keyword

nonn,base

Author

Lekraj Beedassy, Jan 11 2007

Extensions

Corrected by Ray Chandler, Jan 16 2007

Status

approved