A179910 Primes with two embedded primes.

23, 37, 53, 73, 127, 139, 157, 167, 193, 211, 227, 229, 241, 251, 263, 277, 307, 331, 383, 389, 419, 433, 439, 443, 457, 467, 503, 521, 541, 557, 563, 577, 587, 599, 619, 631, 643, 647, 659, 677, 683, 727, 751, 757, 761, 827, 829, 839, 857, 859, 883, 929

Offset

1,1

Comments

It appears that p having n embedded primes means that the set of prime integers generated by contiguous proper substrings of p has size n.

A079066(a(n)) = 2.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Mathematica

f[n_] := Block[ {id = IntegerDigits@n}, len = Length@ id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[ id, k, 1], {k, len}], 1]], True] + 1]; Select[ Prime@ Range@ 160, f@# == 3 &]
Select[ Prime@ Range@ 160, Function[ n, Length@ Select[ Union[ FromDigits /@ (Flatten[ Table[ Partition[#, k, 1], {k, Length@ # - 1}], 1] &)@ IntegerDigits@ n], PrimeQ]]@ # == 2 &] (* Michael Somos, Jan 13 2011 *)

Prog

(Haskell)
import Data.List (elemIndices)
a179910 n = a179910_list !! (n-1)
a179910_list = map (a000040 . (+ 1)) $ elemIndices 2 a079066_list
-- Reinhard Zumkeller, Jul 19 2011

Crossrefs

Cf. A039996, A079397, A033274, A034844, A092621, A179909 - A179919, A033274.

Sequence in context: A348699 A092622 A129351 * A124888 A141521 A080906

Adjacent sequences: A179907 A179908 A179909 * A179911 A179912 A179913

Keyword

base,nonn

Author

Robert G. Wilson v, Aug 01 2010

Status

approved