A245193 -id:A245193 - cp's OEIS frontend

A091633 Primes having only {1, 3, 7, 9} as digits.

3, 7, 11, 13, 17, 19, 31, 37, 71, 73, 79, 97, 113, 131, 137, 139, 173, 179, 191, 193, 197, 199, 311, 313, 317, 331, 337, 373, 379, 397, 719, 733, 739, 773, 797, 911, 919, 937, 971, 977, 991, 997, 1117, 1171, 1193, 1319, 1373, 1399, 1733, 1777, 1913, 1931, 1933

Offset: 1

Enoch Haga, Jan 26 2004

Some primes of sufficient length might be termed DNA primes if the sequence of digits 1,3,7,9 in any order happens to be an appropriate analog of the DNA bases A, G, C, T. It would be interesting to know if it is possible for any DNA sequence to match a DNA prime.

Pierre Cami and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (first 5058 terms from Pierre Cami)
Index to entries for primes with digits in a given set

Subsequence of A136333, A245193, and A030096.
A091871 gives prime index.
Cf. A010051.

a091633 n = a091633_list !! (n-1)
a091633_list = filter ((== 1) . a010051') a136333_list
-- Reinhard Zumkeller, Jul 17 2014

Select[Flatten[Table[FromDigits/@Tuples[{1,3,7,9},n],{n,4}]],PrimeQ] (* Harvey P. Dale, Jun 26 2015 *)

Select primes having digits 1, 3, 7, 9 only.

a(n) = A000040(A091871(n)). - R. J. Mathar, Aug 29 2018

A136333 Numbers containing only digits coprime to 10 in their decimal representation.

Original entry on oeis.org

1, 3, 7, 9, 11, 13, 17, 19, 31, 33, 37, 39, 71, 73, 77, 79, 91, 93, 97, 99, 111, 113, 117, 119, 131, 133, 137, 139, 171, 173, 177, 179, 191, 193, 197, 199, 311, 313, 317, 319, 331, 333, 337, 339, 371, 373, 377, 379, 391, 393, 397, 399, 711, 713, 717, 719, 731

Offset: 1

Reinhard Zumkeller, Mar 26 2008

Numbers containing digits 1,3,7,9 only, or, numbers written in base 4 (cf. A007090) with digits mapped by: 0->1, 1->3, 2->7 and 3->9. - Reinhard Zumkeller, Jul 17 2014

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
Index entries for 10-automatic sequences.

Cf. A007090, A091633 (primes), A245193.

import Data.List (intersect)
a136333 n = a136333_list !! (n-1)
a136333_list = filter (null . intersect "024568" . show) [1..]
-- Reinhard Zumkeller, Jul 17 2014

fQ[n_] := Block[{s = {1, 3, 7, 9}}, Union[Join[s, IntegerDigits@ n]] == s]; Select[ Range@ 1000, fQ] (* or *)
depth = 3; FromDigits@# & /@ FlattenAt[ Table[ Tuples[{1, 3, 7, 9}, n], {n, depth}], {#} & /@ Range[depth]] (* Robert G. Wilson v, Jul 02 2014 *)

isok(m) = my(d=digits(m)); apply(x->gcd(x, 10), d) == vector(#d, k, 1); \\ Michel Marcus, Feb 25 2022

Sum_{n>=1} 1/a(n) = 2.395867871130444522329053889312125689319669370758630349552737883715872077555... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 15 2024

A338715 Smallest prime ending with decimal expansion of n, for n relatively prime to 10.

Original entry on oeis.org

11, 3, 7, 19, 11, 13, 17, 19, 421, 23, 127, 29, 31, 233, 37, 139, 41, 43, 47, 149, 151, 53, 157, 59, 61, 163, 67, 269, 71, 73, 277, 79, 181, 83, 487, 89, 191, 193, 97, 199, 101, 103, 107, 109, 2111, 113, 1117, 3119, 3121, 1123, 127, 1129, 131, 4133, 137, 139, 2141, 2143, 5147, 149, 151, 1153, 157

Offset: 1

N. J. A. Sloane, Nov 11 2020

a(n) exists by Dirichlet's theorem.

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for primes involving decimal expansion of n

Cf. A045572, A105888 (base 2 equivalent), A258190.

See A245193, A337834, A338716 for other versions.

N:= 100: # for a(1) to a(N)
V:= Vector(N):
count:= 0:
for n from 1 while count < N do
  if igcd(n,10)=1 then
    count:= count+1;
    d:= ilog10(n)+1;
    for x from n by 10^d do
      if isprime(x) then V[count]:= x; break fi
    od
  fi
od:
convert(V,list); # Robert Israel, Nov 11 2020

from sympy import isprime
def a(n):
    ending = 2*n - 1 + (n+1)//4 * 2 # A045572
    i, pow10 = ending, 10**len(str(ending))
    while not isprime(i): i += pow10
    return i
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Nov 03 2021

More terms from Robert Israel, Nov 11 2020

A338716 Smallest prime ending with decimal expansion of n, for n equal to 5 or relatively prime to 10.

Original entry on oeis.org

11, 3, 5, 7, 19, 11, 13, 17, 19, 421, 23, 127, 29, 31, 233, 37, 139, 41, 43, 47, 149, 151, 53, 157, 59, 61, 163, 67, 269, 71, 73, 277, 79, 181, 83, 487, 89, 191, 193, 97, 199, 101, 103, 107, 109, 2111, 113, 1117, 3119, 3121, 1123, 127, 1129, 131, 4133, 137, 139, 2141, 2143, 5147, 149, 151, 1153, 157

Offset: 1

N. J. A. Sloane, Nov 11 2020

Included for completeness. This is A338715 with 5 adjoined. See that entry for further information.

a(n) exists by Dirichlet's theorem.

Index entries for primes involving decimal expansion of n

See A245193, A337834, A338715 for other versions.

More terms from Robert Israel, Nov 11 2020

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A091633 Primes having only {1, 3, 7, 9} as digits.

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A136333 Numbers containing only digits coprime to 10 in their decimal representation.

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A338715 Smallest prime ending with decimal expansion of n, for n relatively prime to 10.

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A338716 Smallest prime ending with decimal expansion of n, for n equal to 5 or relatively prime to 10.

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