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A094535
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a(n) is the smallest integer m such that A039995(m)=n.
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3
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1, 2, 13, 23, 113, 131, 137, 1013, 1031, 1273, 1237, 1379, 6173, 10139, 10193, 10379, 10397, 10937, 12397, 12379, 36137, 36173, 101397, 102371, 101937, 102973, 103917, 106937, 109371, 109739, 123797, 123917, 123719, 346137, 193719, 346173
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Giovanni Resta, Table of n, a(n) for n = 0..500 (first 101 terms from Reinhard Zumkeller)
Carlos Rivera, Puzzle 265. Primes embedded, The Prime Puzzles & Problems Connection.
Reinhard Zumkeller, Illustration of initial terms
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FORMULA
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A039995(a(n)) = n and A039995(m) != n for m < a(n). - Reinhard Zumkeller, Feb 01 2012
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EXAMPLE
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a(6) = 137 because 137 is the smallest number m such that A039995(m) = 6; the six numbers 3, 7, 13, 17, 37 & 137 are primes.
See also A205956 for a(100) = 39467139.
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MATHEMATICA
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cnt[n_] := Count[ PrimeQ@ Union[ FromDigits /@ Subsets[ IntegerDigits[n]]], True]; a[n_] := Block[{k = 1}, While[cnt[k] != n, k++]; k]; Array[a, 21, 0] (* Giovanni Resta, Jun 16 2017 *)
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PROG
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(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a094535 n = a094535_list !! n
a094535_list = map ((+ 1) . fromJust . (`elemIndex` a039995_list)) [0..]
-- Reinhard Zumkeller, Feb 01 2012
(Python)
from sympy import isprime
from itertools import chain, combinations as combs, count, islice
def powerset(s): # nonempty subsets of s
return chain.from_iterable(combs(s, r) for r in range(1, len(s)+1))
def A039995(n):
ss = set(int("".join(s)) for s in powerset(str(n)))
return sum(1 for k in ss if isprime(k))
def agen():
adict, n = dict(), 0
for k in count(1):
v = A039995(k)
if v not in adict: adict[v] = k
while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 36))) # Michael S. Branicky, Aug 07 2022
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CROSSREFS
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Cf. A039995, A093301, A039997.
Cf. A205956.
Sequence in context: A215390 A285789 A090528 * A035244 A085822 A213321
Adjacent sequences: A094532 A094533 A094534 * A094536 A094537 A094538
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KEYWORD
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base,nonn
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AUTHOR
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Farideh Firoozbakht, May 08 2004
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STATUS
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approved
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