

A033274


Primes that do not contain any other prime as a proper substring.


26



2, 3, 5, 7, 11, 19, 41, 61, 89, 101, 109, 149, 181, 401, 409, 449, 491, 499, 601, 691, 809, 881, 991, 1009, 1049, 1069, 1481, 1609, 1669, 1699, 1801, 4001, 4049, 4481, 4649, 4801, 4909, 4969, 6091, 6469, 6481, 6869, 6949, 8009, 8069, 8081, 8609, 8669, 8681
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OFFSET

1,1


COMMENTS

If there is more than one digit, all digits must be nonprime numbers.
A179335(n) = prime(n) iff prime(n) is in this sequence. For n > 4, prime(n) is in this sequence iff A109066(n) = 0.  Reinhard Zumkeller, Jul 11 2010, corrected by M. F. Hasler, Aug 27 2012
A079066(n) = 0 iff prime(n) is in this sequence. [Corrected by M. F. Hasler, Aug 27 2012]
What are the asymptotics of this sequence?  Charles R Greathouse IV, Aug 27 2012


LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000.


EXAMPLE

149 is a term as 1,4,9,14,49 are all nonprimes. 199 is not a member as 19 is a prime.


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@ 1100, f@# == 1 &] (* Robert G. Wilson v, Aug 01 2010 *)


PROG

(Haskell)
import Data.List (elemIndices)
a033274 n = a033274_list !! (n1)
a033274_list = map (a000040 . (+ 1)) $ elemIndices 0 a079066_list
 Reinhard Zumkeller, Jul 19 2011


CROSSREFS

Cf. A089768, A089770, A039996, A079397, A033274, A034844, A179909A179919.
Sequence in context: A118985 A092728 A089769 * A071062 A320725 A320771
Adjacent sequences: A033271 A033272 A033273 * A033275 A033276 A033277


KEYWORD

base,nonn


AUTHOR

Michael Kleber


EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Luca Colucci, Apr 03 2008


STATUS

approved



