A036953 -id:A036953 - cp's OEIS frontend

A261267 Primes having only {0, 2, 7} as digits.

2, 7, 227, 277, 727, 2027, 2207, 2707, 2777, 7027, 7207, 7727, 20707, 22027, 22277, 22727, 22777, 27077, 27277, 70207, 72077, 72227, 72277, 72707, 72727, 200227, 202277, 202777, 207227, 222007, 222707, 227027, 227207, 227707, 272227, 272777, 277007

Offset: 1

Vincenzo Librandi, Aug 13 2015

A020459 is a subsequence.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Cf. Primes that contain only the digits (0,2,k): A036953 (k=1), A260125 (k=3), this sequence (k=7), A261268 (k=9).

Cf. A000040, A020459.

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0, 2, 7]];

Select[Prime[Range[6 10^4]], Complement[IntegerDigits[#], {0, 2, 7}] == {}&]

A106100 Primes with maximal digit = 2.

Original entry on oeis.org

2, 211, 1021, 1201, 2011, 2111, 2221, 10211, 12011, 12101, 12211, 20011, 20021, 20101, 20201, 21001, 21011, 21101, 21121, 21211, 21221, 22111, 101021, 101221, 102001, 102101, 102121, 110221, 111121, 111211, 112111, 112121, 120011, 120121

Offset: 1

Zak Seidov, May 07 2005

Subsequence of A036953. Prime numbers p such that A209928(p) = 2. Complement of A221698 with respect to A221697. [Jaroslav Krizek, Jan 22 2013]

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A106093, A106094, A106095, A106096, A106097, A106098, A106099.

N:= 6: # to get all terms of up to N digits
M2:= {1};M1:= {1}:
for d from 1 to N-1 do
  M2:= map(t -> (t, t+10^d, t+2*10^d), M2);
  M1:= map(t -> (t, t+10^d), M1);
od:
sort(convert({2} union select(isprime,M2 minus M1),list)); # Robert Israel, Jun 19 2016

Select[Prime[Range[10000]], Max[IntegerDigits[ # ]]==2&]

isok(p) = isprime(p) && (vecmax(digits(p)) == 2); \\ Michel Marcus, Jan 02 2019

More terms from Rick L. Shepherd, May 22 2005

A107715 Primes having only {0,1,2,3} as digits.

Original entry on oeis.org

2, 3, 11, 13, 23, 31, 101, 103, 113, 131, 211, 223, 233, 311, 313, 331, 1013, 1021, 1031, 1033, 1103, 1123, 1201, 1213, 1223, 1231, 1301, 1303, 1321, 2003, 2011, 2111, 2113, 2131, 2203, 2213, 2221, 2311, 2333, 3001, 3011, 3023, 3121, 3203, 3221, 3301, 3313

Offset: 1

Rick L. Shepherd, May 22 2005

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)

Subsequence of A036956.
Cf. A036953 (primes containing digits from set {0, 1, 2}).
Cf. A010051, A007090, A193890, A385776.

a107715 n = a107715_list !! (n-1)
a107715_list = filter ((== 1) . a010051) a007090_list
-- Reinhard Zumkeller, Aug 11 2011

Select[Prime[Range[500]],Max[IntegerDigits[#]]<4&] (* Harvey P. Dale, May 09 2012 *)
Select[FromDigits/@Tuples[{0,1,2,3},4],PrimeQ] (* Harvey P. Dale, Mar 06 2016 *)

from gmpy2 import digits
from sympy import isprime
[int(digits(n,4)) for n in range(1000) if isprime(int(digits(n,4)))] # Chai Wah Wu, Jul 31 2014

print(list(islice(primes_with("0123"), 41))) # uses function/imports in A385776. Jason Bard, Jul 18 2025

A036954 Primes with digits in {0,1,2} taken as base 3 and converted to base 10.

Original entry on oeis.org

2, 4, 10, 22, 34, 46, 58, 67, 79, 94, 103, 139, 145, 157, 166, 169, 172, 181, 190, 193, 199, 205, 211, 214, 229, 277, 283, 295, 298, 307, 313, 349, 367, 373, 391, 394, 409, 421, 433, 439, 463, 466, 478, 505, 517, 523, 529, 535, 541, 547, 556, 559, 571, 577

Offset: 1

Patrick De Geest, Jan 04 1999

Equivalently: terms of A036953 read in base 3 (and written in base 10). - M. F. Hasler, Jul 25 2015

Equivalently, k such that A007089(k), read literally as a decimal number, is a prime. - N. J. A. Sloane, Feb 17 2023

			a(n) = 313 is 102121{3}, and 102121{10} is prime.

Cf. A036952-A036964.

Indices of primes in A007089.

FromDigits[#,3]&/@Select[Tuples[{0,1,2},6],PrimeQ[FromDigits[#]]&] (* Harvey P. Dale, Mar 27 2021 *)

is(n)=(n%3==1||n==2)&&isprime((n=digits(n,3))*vectorv(#n,i,10^(#n-i))) \\ M. F. Hasler, Jul 25 2015

a(n) == 1 (mod 3) for all n > 1. - M. F. Hasler, Jul 25 2015

Offset corrected to 1 and minor edits by M. F. Hasler, Jul 25 2015

A111488 Primes having only {0, 1, 3, 6} as digits.

Original entry on oeis.org

3, 11, 13, 31, 61, 101, 103, 113, 131, 163, 311, 313, 331, 601, 613, 631, 661, 1013, 1031, 1033, 1061, 1063, 1103, 1163, 1301, 1303, 1361, 1601, 1613, 1663, 3001, 3011, 3061, 3163, 3301, 3313, 3331, 3361, 3613, 3631, 6011, 6101, 6113, 6131, 6133, 6163

Offset: 1

Jonathan Vos Post, Nov 15 2005

Includes all repunit primes (A004022). Conjecture: an infinite sequence. Note twin primes: (11, 13), (101, 103), (311, 313), (1031, 1033), (1061, 1063), (1301, 1303), (6131, 6133), (10301, 10303), (10331, 10333), (13001, 13003).
In other words, primes with digits in the set {0,1,3,6}. - M. F. Hasler, Jul 25 2015
The number of 1's in the representation must be either 1 or 2 (mod 3), because otherwise the number would be divisible by 3 (and therefore composite). The only exception is the 3 itself. This excludes basically members of A038603. - R. J. Mathar, Jul 25 2015

Robert Israel, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Cf. A000040, A000217, A004022, A038603.

Cf. also A020450 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

f:= proc(x) local L,p;
  L:= subs([3=6,2=3],convert(x,base,4));
  p:= add(L[i]*10^(i-1),i=1..nops(L));
  if isprime(p) then p fi
end proc:
map(f, [$1..4^4]); # Robert Israel, Dec 18 2018

Select[Prime@ Range@ 1000, SubsetQ[{0, 1, 3, 6}, IntegerDigits@ #] &] (* Michael De Vlieger, Jul 25 2015 *)

A111488={(n, show=0, L=[0,1,3,6])->my(t); for(d=1,1e9,u=vector(d, i, 10^(d-i))~; forvec(v=vector(d,i,[1+(i==1&&!L[1]), #L]), ispseudoprime(t=vector(d, i, L[v[i]])*u)||next; show&print1(t", "); n--||return(t)))} \\ M. F. Hasler, Jul 25 2015

Corrected by Ray Chandler, Nov 19 2005

Name changed by Sean A. Irvine, Jul 21 2025

A385344 Numbers where all the digits of all the prime factors are smaller than 3.

Original entry on oeis.org

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 101, 121, 128, 176, 202, 211, 242, 256, 352, 404, 422, 484, 512, 704, 808, 844, 968, 1021, 1024, 1111, 1201, 1331, 1408, 1616, 1688, 1936, 2011, 2042, 2048, 2111, 2221, 2222, 2321, 2402, 2662, 2816, 3232, 3376, 3872, 4022, 4084, 4096, 4222, 4442, 4444, 4642, 4804, 5324, 5632

Offset: 1

Jens Ahlström, Jun 26 2025

Multiplicative closure of A036953.

			202 is in the sequence since the prime factors 2 and 101 both have all digits smaller than 3.
34 is not in the sequence since it has the prime factor 17 that have a digit larger than 2.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Supersequence of A036953. Cf. A385345.

A385344Q[k_] := AllTrue[FactorInteger[k][[All, 1]], Max[IntegerDigits[#]] < 3 &];
Select[Range[10000], A385344Q] (* Paolo Xausa, Jun 28 2025 *)

from sympy import primefactors
def ok(n): return all(set(str(f)) <= set("012") for f in primefactors(n))
print([k for k in range(1, 6000) if ok(k)]) # Michael S. Branicky, Jun 26 2025

{k | all prime factors of k are in A036953}. - Michael S. Branicky, Jun 26 2025

A386017 Primes having only {0, 1, 2, 4} as digits.

Original entry on oeis.org

2, 11, 41, 101, 211, 241, 401, 421, 1021, 1201, 2011, 2111, 2141, 2221, 2411, 2441, 4001, 4021, 4111, 4201, 4211, 4241, 4421, 4441, 10111, 10141, 10211, 11411, 12011, 12041, 12101, 12211, 12241, 12401, 12421, 14011, 14221, 14401, 14411, 20011, 20021, 20101, 20201

Offset: 1

Jason Bard, Jul 14 2025

Subsequence of A036956.
Supersequence of A036953, A260266, A260267.
Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 4]];

Select[FromDigits /@ Tuples[{0, 1, 2, 4}, n], PrimeQ]

primes_with(, 1, [0, 1, 2, 4]) \\ uses function in A385776

print(list(islice(primes_with("0124"), 41))) # uses function/imports in A385776

A386018 Primes having only {0, 1, 2, 5} as digits.

Original entry on oeis.org

2, 5, 11, 101, 151, 211, 251, 521, 1021, 1051, 1151, 1201, 1511, 2011, 2111, 2221, 2251, 2521, 2551, 5011, 5021, 5051, 5101, 5501, 5521, 10111, 10151, 10211, 10501, 11251, 11551, 12011, 12101, 12211, 12251, 12511, 15101, 15121, 15511, 15551, 20011, 20021, 20051

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A036953, A199325, A385773.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 5]];

Select[FromDigits /@ Tuples[{0, 1, 2, 5}, n], PrimeQ]

primes_with(, 1, [0, 1, 2, 5]) \\ uses function in A385776

print(list(islice(primes_with("0125"), 41))) # uses function/imports in A385776

A386019 Primes having only {0, 1, 2, 6} as digits.

Original entry on oeis.org

2, 11, 61, 101, 211, 601, 661, 1021, 1061, 1201, 1601, 1621, 2011, 2111, 2161, 2221, 2621, 6011, 6101, 6121, 6211, 6221, 6661, 10061, 10111, 10211, 10601, 11161, 11261, 11621, 12011, 12101, 12161, 12211, 12601, 12611, 16001, 16061, 16111, 16661, 20011, 20021

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A036953, A199326, A285774.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 6]];

Select[FromDigits /@ Tuples[{0, 1, 2, 6}, n], PrimeQ]

primes_with(, 1, [0, 1, 2, 6]) \\ uses function in A385776

print(list(islice(primes_with("0126"), 41))) # uses function/imports in A385776

A386020 Primes having only {0, 1, 2, 7} as digits.

Original entry on oeis.org

2, 7, 11, 17, 71, 101, 107, 127, 211, 227, 271, 277, 701, 727, 1021, 1117, 1171, 1201, 1217, 1277, 1721, 1777, 2011, 2017, 2027, 2111, 2207, 2221, 2707, 2711, 2777, 7001, 7027, 7121, 7127, 7177, 7207, 7211, 7717, 7727, 10007, 10111, 10177, 10211, 10271, 10711

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A036953, A199327, A260889.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 7]];

Select[FromDigits /@ Tuples[{0, 1, 2, 7}, n], PrimeQ]

primes_with(, 1, [0, 1, 2, 7]) \\ uses function in A385776

print(list(islice(primes_with("0127"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A261267 Primes having only {0, 2, 7} as digits.

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A106100 Primes with maximal digit = 2.

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A107715 Primes having only {0,1,2,3} as digits.

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A036954 Primes with digits in {0,1,2} taken as base 3 and converted to base 10.

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A111488 Primes having only {0, 1, 3, 6} as digits.

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A385344 Numbers where all the digits of all the prime factors are smaller than 3.

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A386017 Primes having only {0, 1, 2, 4} as digits.

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