A179924 Primes with embedded primes.

13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337

Offset: 1

Author

Robert G. Wilson v, Aug 01 2010

Keywords

• base
• easy
• nonn

Comments

A079066(a(n)) > 0. - Reinhard Zumkeller, Jul 19 2011

Is there a prime such that the previous prime is embedded in it? - Ivan N. Ianakiev, Nov 09 2023. Answer from Amiram Eldar: No. If prime(n) is embedded in prime(n+1) then prime(n+1) has at least one digit more than prime(n), so prime(n+1) > 2 * prime(n). But according to Bertrand's postulate, prime(n+1) < 2*prime(n).

Links

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

Crossrefs

Cf. A039996, A079397, A033274, A034844, A092621, A179909 - A179919, A033274, A179922.

Programs

Haskell

import Data.List (findIndices)
a179924 n = a179924_list !! (n-1)
a179924_list = map (a000040 . (+ 1)) $ findIndices (> 0) a079066_list
-- Reinhard Zumkeller, Jul 19 2011

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@ 68, f@# > 1 &]