A217039 -id:A217039 - cp's OEIS frontend

A036953 Primes having only {0, 1, 2} as digits.

2, 11, 101, 211, 1021, 1201, 2011, 2111, 2221, 10111, 10211, 12011, 12101, 12211, 20011, 20021, 20101, 20201, 21001, 21011, 21101, 21121, 21211, 21221, 22111, 101021, 101111, 101221, 102001, 102101, 102121, 110221, 111121, 111211, 112111

Offset: 1

Patrick De Geest, Jan 04 1999

Number of n-digit terms d(n) = (1, 1, 2, 5, 16, 34, 76, 194, 543, 1469, 4094, 11017, ...); e.g., there are five 4-digit terms: 1021, 1201, 2011, 2111, 2221, hence d(4) = 5. - Zak Seidov, Jun 30 2013

Also, primes in A007089. - M. F. Hasler, Jul 25 2015

Zak Seidov, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
Index to entries for primes with digits in a given set

Subsequence of A107715.
Cf. A036952-A036964.
Cf. A020450 - A020472, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349, A217039, A079651.

Select[FromDigits/@Tuples[{0,1,2},6],PrimeQ] (* Harvey P. Dale, Jul 11 2017 *)

lista(n) = {forprime(p=2, n, if (vecmax(digits(p)) <= 2, print1(p, ", ")))} \\ Michel Marcus, Aug 02 2014

A036953={(n,show=0)->for(d=1,1e9,my(u=vector(d,i,10^(d-i))~);forvec(v=vector(d,i,if(i>1,if(iM. F. Hasler, Jul 25 2015

from gmpy2 import digits
from sympy import isprime
[int(digits(n,3)) for n in range(1000) if isprime(int(digits(n,3)))] # Chai Wah Wu, Jul 31 2014

Edited by M. F. Hasler, Jul 25 2015

A260827 Primes having only {0, 5, 7} as digits.

Original entry on oeis.org

5, 7, 557, 577, 757, 5077, 5507, 5557, 7057, 7507, 7577, 7757, 50077, 50707, 50777, 55057, 57077, 57557, 70507, 75557, 75577, 75707, 77557, 500057, 500777, 505777, 507077, 507557, 507757, 550007, 550577, 550757, 555077, 555557, 555707, 557057, 570077, 575077

Offset: 1

Vincenzo Librandi, Aug 01 2015

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

A020467 is a subsequence.
Cf. Primes that contain only the digits (k,5,7): this sequence (k=0), A260828 (k=1), A214705 (k=2), A087363 (k=3), A217039 (k=4), A260829 (k=6), A260830 (k=8), A260831 (k=9).
Cf. A000040.

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0,5,7]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {0, 5, 7}]=={} &]

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
  n, digits, alst = 0, 1, []
  while len(alst) < terms:
    mpstr = "".join(d*digits for d in "057")
    for mp in multiset_permutations(mpstr, digits):
      if mp[0] == "0": continue
      t = int("".join(mp))
      if isprime(t): alst.append(t)
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(38)) # Michael S. Branicky, May 07 2021

A217124 Semiprimes whose decimal representation has only digits in {4,5,7}.

Original entry on oeis.org

4, 55, 57, 74, 77, 445, 447, 454, 545, 554, 745, 755, 4474, 4555, 4574, 4577, 4747, 4754, 4757, 4777, 5447, 5455, 5545, 5554, 5747, 5755, 5774, 5777, 7445, 7447, 7454, 7555, 7745, 7747, 7754, 44477, 44554, 44557, 44747, 44755, 45447, 45454, 45455, 45457

Offset: 1

Jonathan Vos Post, Sep 26 2012

Crooked semiprimes. This is to A217048 as integers all of whose numerals are written (san serif) with at least one right or acute angle (A214584) are to numbers using only the curved digits 0, 3, 6, 8 and 9 (A072960). This is to crooked primes (A217039) as semiprimes (A001358) are to primes (A000040).

			4555 = 5 * 911 is semiprime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001358, A072960, A214584.

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Flatten[Table[FromDigits /@ Tuples[{4, 5, 7}, n], {n, 5}]], SemiPrimeQ] (* T. D. Noe, Sep 27 2012 *)
Select[Flatten[Table[FromDigits/@Tuples[{4,5,7},n],{n,5}]],PrimeOmega[ #] == 2&] (* Harvey P. Dale, Sep 21 2016 *)

A001358 INTERSECTION A214584.

Corrected and extended by T. D. Noe, Sep 27 2012

A386070 Primes having only {0, 4, 5, 7} as digits.

Original entry on oeis.org

5, 7, 47, 457, 547, 557, 577, 757, 4007, 4057, 4447, 4457, 4507, 4547, 5077, 5407, 5477, 5507, 5557, 7057, 7457, 7477, 7507, 7547, 7577, 7757, 40507, 40577, 44507, 44777, 45007, 45077, 45557, 45707, 45757, 47057, 47407, 47507, 47777, 50047, 50077, 50707, 50777

Offset: 1

Jason Bard, Jul 16 2025

Supersequence of A217039, A260827, A384449.

Cf. A000040, A030432, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 4, 5, 7]];

Select[FromDigits /@ Tuples[{0, 4, 5, 7}, n], PrimeQ]

primes_with(, 1, [0, 4, 5, 7]) \\ uses function in A385776

print(list(islice(primes_with("0457"), 41))) # uses function/imports in A385776

A386120 Primes having only {1, 4, 5, 7} as digits.

Original entry on oeis.org

5, 7, 11, 17, 41, 47, 71, 151, 157, 457, 541, 547, 557, 571, 577, 751, 757, 1117, 1151, 1171, 1447, 1451, 1471, 1511, 1571, 1741, 1747, 1777, 4111, 4157, 4177, 4441, 4447, 4451, 4457, 4517, 4547, 4751, 5147, 5171, 5417, 5441, 5471, 5477, 5557, 5711, 5717, 5741

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A079651, A217039, A260268, A260828.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 4, 5, 7]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 4, 5, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 4, 5, 7]) \\ uses function in A385776

print(list(islice(primes_with("1457"), 41))) # uses function/imports in A385776

A386153 Primes having only {2, 4, 5, 7} as digits.

Original entry on oeis.org

2, 5, 7, 47, 227, 257, 277, 457, 547, 557, 577, 727, 757, 2447, 2477, 2557, 2777, 4447, 4457, 4547, 5227, 5477, 5527, 5557, 7247, 7457, 7477, 7547, 7577, 7727, 7757, 22247, 22277, 22447, 22727, 22777, 24247, 24527, 24547, 25247, 25447, 25457, 25577, 25747, 27277

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A214705, A217039, A385784.

Cf. A000040, A030432, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 4, 5, 7]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 4, 5, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 4, 5, 7]) \\ uses function in A385776

print(list(islice(primes_with("2457"), 41))) # uses function/imports in A385776

A386170 Primes having only {3, 4, 5, 7} as digits.

Original entry on oeis.org

3, 5, 7, 37, 43, 47, 53, 73, 337, 347, 353, 373, 433, 443, 457, 547, 557, 577, 733, 743, 757, 773, 3343, 3347, 3373, 3433, 3457, 3533, 3547, 3557, 3733, 4337, 4357, 4373, 4447, 4457, 4547, 4733, 5333, 5347, 5437, 5443, 5477, 5557, 5573, 5737, 5743, 7333, 7433

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A087363, A199345, A199347, A217039.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [3, 4, 5, 7]];

Flatten[Table[Select[FromDigits /@ Tuples[{3, 4, 5, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [3, 4, 5, 7]) \\ uses function in A385776

print(list(islice(primes_with("3457"), 41))) # uses function/imports in A385776

A386188 Primes having only {4, 5, 6, 7} as digits.

Original entry on oeis.org

5, 7, 47, 67, 457, 467, 547, 557, 577, 647, 677, 757, 4447, 4457, 4547, 4567, 4657, 5477, 5557, 5647, 5657, 6547, 6577, 7457, 7477, 7547, 7577, 7757, 44647, 44657, 44777, 45557, 45667, 45677, 45757, 45767, 46447, 46457, 46477, 46567, 46747, 46757, 47657, 47777

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A217039, A260829, A385794.

Cf. A000040, A030432, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 5, 6, 7]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 5, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 5, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("4567"), 41))) # uses function/imports in A385776

A386190 Primes having only {4, 5, 7, 8} as digits.

Original entry on oeis.org

5, 7, 47, 457, 487, 547, 557, 577, 587, 757, 787, 857, 877, 887, 4447, 4457, 4547, 4787, 4877, 5477, 5557, 5857, 7457, 7477, 7487, 7547, 7577, 7757, 7877, 8447, 8747, 8887, 44587, 44777, 44887, 45557, 45587, 45757, 45887, 47777, 47857, 48487, 48757, 48787, 48847

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A217039, A260830, A385795.

Cf. A000040, A030432, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 5, 7, 8]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 5, 7, 8}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 5, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("4578"), 41))) # uses function/imports in A385776

A386191 Primes having only {4, 5, 7, 9} as digits.

Original entry on oeis.org

5, 7, 47, 59, 79, 97, 449, 457, 479, 499, 547, 557, 577, 599, 757, 797, 947, 977, 997, 4447, 4457, 4547, 4549, 4597, 4759, 4799, 4957, 4999, 5449, 5477, 5479, 5557, 5749, 5779, 7457, 7459, 7477, 7499, 7547, 7549, 7559, 7577, 7757, 7759, 7949, 9479, 9497, 9547

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A217039, A260831, A261183, A385793.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 5, 7, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 5, 7, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 5, 7, 9]) \\ uses function in A385776

print(list(islice(primes_with("4579"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A036953 Primes having only {0, 1, 2} as digits.

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A260827 Primes having only {0, 5, 7} as digits.

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A217124 Semiprimes whose decimal representation has only digits in {4,5,7}.

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A386070 Primes having only {0, 4, 5, 7} as digits.

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A386120 Primes having only {1, 4, 5, 7} as digits.

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A386153 Primes having only {2, 4, 5, 7} as digits.

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A386170 Primes having only {3, 4, 5, 7} as digits.

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