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A033274
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Primes that do not contain any other prime as a proper substring.
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26
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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)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)
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EXAMPLE
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149 is a term as 1, 4, 9, 14, 49 are all nonprimes.
199 is not a term as 19 is a prime.
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MATHEMATICA
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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 *)
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PROG
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(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
(Python)
from sympy import isprime
def ok(n):
if n in {2, 3, 5, 7}: return True
s = str(n)
if set(s) & {"2", "3", "5", "7"} or not isprime(n): return False
ss2 = set(s[i:i+l] for i in range(len(s)-1) for l in range(2, len(s)))
return not any(isprime(int(ss)) for ss in ss2)
print([k for k in range(9000) if ok(k)]) # Michael S. Branicky, Jun 29 2022
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CROSSREFS
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Cf. A089768, A089770, A039996, A079397, A033274, A034844, A179909-A179919.
Sequence in context: A118985 A092728 A089769 * A071062 A320725 A320771
Adjacent sequences: A033271 A033272 A033273 * A033275 A033276 A033277
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KEYWORD
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base,nonn
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AUTHOR
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Michael Kleber
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EXTENSIONS
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Edited by N. J. A. Sloane at the suggestion of Luca Colucci, Apr 03 2008
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STATUS
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approved
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