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A033274 Primes that do not contain any other prime as a substring. 25
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 (list; graph; refs; listen; history; text; internal format)
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 !! (n-1)

a033274_list = map (a000040 . (+ 1)) $ elemIndices 0 a079066_list

-- Reinhard Zumkeller, Jul 19 2011

CROSSREFS

Cf. A089768, A089770, A039996, A079397, A033274, A034844, A179909-A179919.

Sequence in context: A118985 A092728 A089769 * A071062 A002231 A087769

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

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Last modified March 28 02:40 EDT 2017. Contains 284182 sequences.