A020459 -id:A020459 - cp's OEIS frontend

A260889 Primes having only {1, 2, 7} as digits.

2, 7, 11, 17, 71, 127, 211, 227, 271, 277, 727, 1117, 1171, 1217, 1277, 1721, 1777, 2111, 2221, 2711, 2777, 7121, 7127, 7177, 7211, 7717, 7727, 11117, 11171, 11177, 11717, 11777, 12211, 12227, 12277, 12721, 17117, 21121, 21211, 21221, 21227, 21277, 21727

Offset: 1

Vincenzo Librandi, Aug 04 2015

A020450, A020455 and A020459 are subsequences.

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 (k,1,7): A199327 (k=0), this sequence (k=2), A260379 (k=3), A079651 (k=4), A260828 (k=5), A260891 (k=6), A260892 (k=8), A260893 (k=9).

Cf. A020450, A020455, A020459.

[p: p in PrimesUpTo(3*10^4) | Set(Intseq(p)) subset [1, 2, 7]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {1, 2, 7}] == {} &]
Table[Select[FromDigits/@Tuples[{1,2,7},n],PrimeQ],{n,5}]//Flatten (* Harvey P. Dale, Apr 12 2018 *)

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

Original entry on oeis.org

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}] == {}&]

A261182 Primes having only {2, 7, 9} as digits.

Original entry on oeis.org

2, 7, 29, 79, 97, 227, 229, 277, 727, 797, 929, 977, 997, 2297, 2729, 2777, 2797, 2927, 2999, 7229, 7297, 7727, 7927, 9227, 9277, 9929, 22229, 22277, 22279, 22727, 22777, 27277, 27299, 27779, 27799, 27997, 29297, 29927, 72227, 72229, 72277, 72727, 72797

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020459, A020460 and A020471 are subsequences.

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Chai Wah Wu)
Index to entries for primes with digits in a given set

Cf. similar sequences listed in A261181.

Cf. A000040, A020459, A020460, A020471, A385776.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [2, 7, 9]];

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {2, 7, 9}] == {} &]
Select[Flatten[Table[FromDigits/@Tuples[{2,7,9},n],{n,5}]],PrimeQ] (* Harvey P. Dale, Dec 17 2024 *)

from gmpy2 import is_prime
from itertools import product
A261182_list = [int(''.join(d)) for l in range(1,10) for d in product('279',repeat=l) if is_prime(int(''.join(d)))] # Chai Wah Wu, Aug 11 2015

A385784 Primes having only {2, 4, 7} as digits.

Original entry on oeis.org

2, 7, 47, 227, 277, 727, 2447, 2477, 2777, 4447, 7247, 7477, 7727, 22247, 22277, 22447, 22727, 22777, 24247, 27277, 27427, 42227, 42727, 44777, 47777, 72227, 72277, 72727, 74747, 77447, 77477, 77747, 222247, 242227, 242447, 242747, 244247, 244747, 272227

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020459, A020465.

Cf. A000040, A030432, A385776.

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

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

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

print(list(islice(primes_with("247"), 41))) # uses function/imports in A385776

A385787 Primes having only {2, 6, 7} as digits.

Original entry on oeis.org

2, 7, 67, 227, 277, 677, 727, 2267, 2677, 2767, 2777, 6277, 7727, 22277, 22727, 22777, 26227, 26267, 26627, 26777, 27277, 27767, 62627, 67777, 72227, 72277, 72727, 72767, 76667, 76777, 77267, 226267, 226777, 227267, 227627, 262627, 266677, 266767, 267227

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020459, A020469.

Cf. A000040, A030432, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{2, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("267"), 41))) # uses function/imports in A385776

A385789 Primes having only {2, 7, 8} as digits.

Original entry on oeis.org

2, 7, 227, 277, 727, 787, 827, 877, 887, 2287, 2777, 2887, 7727, 7877, 8287, 8887, 22277, 22727, 22777, 22787, 22877, 27277, 27827, 28277, 72227, 72277, 72287, 72727, 78277, 78787, 78877, 78887, 82727, 82787, 87277, 87877, 87887, 222787, 222877, 227827, 228887

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020459, A020470.

Cf. A000040, A030432, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 7, 8]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 7, 8}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("278"), 41))) # uses function/imports in A385776

A284921 Numbers with digits 2 and 7 only.

Original entry on oeis.org

2, 7, 22, 27, 72, 77, 222, 227, 272, 277, 722, 727, 772, 777, 2222, 2227, 2272, 2277, 2722, 2727, 2772, 2777, 7222, 7227, 7272, 7277, 7722, 7727, 7772, 7777, 22222, 22227, 22272, 22277, 22722, 22727, 22772, 22777, 27222, 27227, 27272, 27277, 27722, 27727

Offset: 1

Jaroslav Krizek, Apr 05 2017

Prime terms are in A020459.

Cf. Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), A284920 (k = 4), A072961 (k = 5), A284632 (k = 6), this sequence (k = 7), A284922 (k = 8), A284923 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 7}]

Flatten@ Array[FromDigits /@ Tuples[{2, 7}, #] &, 5] (* Michael De Vlieger, Apr 06 2017 *)

A329760 Primes without {2, 7} as digits.

Original entry on oeis.org

3, 5, 11, 13, 19, 31, 41, 43, 53, 59, 61, 83, 89, 101, 103, 109, 113, 131, 139, 149, 151, 163, 181, 191, 193, 199, 311, 313, 331, 349, 353, 359, 383, 389, 401, 409, 419, 431, 433, 439, 443, 449, 461, 463, 491, 499, 503, 509, 541, 563, 569, 593, 599, 601, 613

Offset: 1

Alois P. Heinz, Nov 20 2019

Alois P. Heinz, Table of n, a(n) for n = 1..20000
Marianne Freiberger, Primes without 7s.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
Index to entries for primes with digits in a given set

Cf. A000040, A020459, A038604, A038615.

[p: p in PrimesUpTo(700) | not 2 in Intseq(p) and not 7 in Intseq(p) ]; // Vincenzo Librandi, Jan 02 2020

Select[Prime[Range[120]], DigitCount[#, 10, 2]==0 && DigitCount[#, 10, 7]==0 &] (* Vincenzo Librandi, Jan 02 2020 *)

{ A038604 } intersect { A038615 }.

A036312 Composite numbers whose prime factors contain no digits other than 2 and 7.

Original entry on oeis.org

4, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 128, 196, 224, 256, 343, 392, 448, 454, 512, 554, 686, 784, 896, 908, 1024, 1108, 1372, 1454, 1568, 1589, 1792, 1816, 1939, 2048, 2216, 2401, 2744, 2908, 3136, 3178, 3584, 3632, 3878, 4096, 4432, 4802, 5089, 5488

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020459. - David A. Corneth, Oct 09 2020

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 5340 terms from Robert Israel)
Index entries for sequences related to prime factors.

Cf. A003591, A020459, A036302-A036325.

dmax:= 4: # for terms < 2*10^dmax
P:= {2,7}:
L:= {7}:
for d from 1 to dmax-1 do
  L:= map(t -> 2*10^d+t, L) union map(t -> 7*10^d+t, L);
  P:= P union select(isprime,L);
od:
R:= {1}: N:= 2*10^dmax:
for p in P do
  R:= R union map(t -> seq(t*p^j,j=1..floor(log[p](N/t))), R)
od:
sort(convert(R minus P minus {1},list)); # Robert Israel, Aug 04 2020

Sum_{n>=1} 1/a(n) = Product_{p in A020459} (p/(p - 1)) - Sum_{p in A020459} 1/p - 1 = 0.7041098484... . - Amiram Eldar, May 18 2022

A036938 Smallest n-digit prime containing only digits 2 and 7, or 0 if no such prime exists.

Original entry on oeis.org

2, 0, 227, 2777, 22277, 272227, 2227727, 22227277, 222222227, 2222222777, 22222222277, 222222272777, 2222222227727, 22222222777277, 222222222222227, 2222222222227727, 22222222222227227, 222222222227227727

Offset: 1

Patrick De Geest, Jan 04 1999

Jinyuan Wang, Table of n, a(n) for n = 1..500

Cf. A020459, A036229, A036312.

cp's OEIS Frontend

A260889 Primes having only {1, 2, 7} as digits.

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

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A261182 Primes having only {2, 7, 9} as digits.

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A385784 Primes having only {2, 4, 7} as digits.

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A385787 Primes having only {2, 6, 7} as digits.

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A385789 Primes having only {2, 7, 8} as digits.

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A284921 Numbers with digits 2 and 7 only.

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Magma

Mathematica

A329760 Primes without {2, 7} as digits.

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