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A179924
Primes with embedded primes.
1
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
1,1
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
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 &]
PROG
(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
KEYWORD
base,easy,nonn
AUTHOR
Robert G. Wilson v, Aug 01 2010
STATUS
approved