A020469 -id:A020469 - cp's OEIS frontend

A260380 Primes having only {3, 6, 7} as digits.

3, 7, 37, 67, 73, 337, 367, 373, 673, 677, 733, 773, 3373, 3637, 3673, 3677, 3733, 3767, 6337, 6367, 6373, 6637, 6673, 6733, 6737, 6763, 7333, 7673, 33377, 33637, 33767, 33773, 36373, 36637, 36677, 36767, 37337, 37363, 37633, 37663, 63337, 63367, 63377, 63667

Offset: 1

Vincenzo Librandi, Aug 01 2015

A020463 and A020469 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. similar sequences listed in A260378.

Cf. A020463, A020469.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [3, 6, 7]];

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {3, 6, 7}]=={} &]
Select[Flatten[Table[FromDigits/@Tuples[{3,6,7},n],{n,5}]],PrimeQ] (* Harvey P. Dale, Apr 13 2022 *)

A260829 Primes having only {5, 6, 7} as digits.

Original entry on oeis.org

5, 7, 67, 557, 577, 677, 757, 5557, 5657, 6577, 7577, 7757, 55667, 56767, 57557, 57667, 65557, 65657, 65677, 65777, 67567, 67577, 67757, 67777, 75557, 75577, 75767, 76667, 76757, 76777, 77557, 555557, 555677, 555767, 557567, 565567, 565667, 566557, 566567

Offset: 1

Vincenzo Librandi, Aug 02 2015

A020467 and A020469 are subsequences.

Alois P. Heinz, 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

Cf. similar sequences listed in A260827.

Cf. A020467, A020469.

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

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 6, 7}] == {} &]

A260891 Primes having only {1, 6, 7} as digits.

Original entry on oeis.org

7, 11, 17, 61, 67, 71, 167, 617, 661, 677, 761, 1117, 1171, 1667, 1777, 6661, 6761, 7177, 7717, 11117, 11161, 11171, 11177, 11617, 11677, 11717, 11777, 16111, 16661, 17117, 17167, 17761, 61667, 61717, 66161, 66617, 67777, 71161, 71167, 71171, 71671

Offset: 1

Vincenzo Librandi, Aug 05 2015

A020454, A020455 and A020469 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, similar sequences listed in A260889.

Cf. A000040, A020454, A020455, A020469.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1, 6, 7]];

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 6, 7}] == {} &]

A261184 Primes having only {6, 7, 9} as digits.

Original entry on oeis.org

7, 67, 79, 97, 677, 769, 797, 967, 977, 997, 6679, 6779, 6967, 6977, 6997, 7669, 7699, 9677, 9679, 9697, 9767, 9769, 9967, 66697, 66797, 66977, 67679, 67699, 67777, 67967, 67979, 69677, 69697, 69767, 69779, 69997, 76667, 76679, 76697, 76777, 77699, 77797

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020469 and A020471 are subsequences.

Alois P. Heinz, 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

Cf. similar sequences listed in A261181.

Cf. A000040, A020469, A020471.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [6, 7, 9]];

Select[Prime[Range[6 10^4]], Complement[IntegerDigits[#], {6, 7, 9}] == {} &]
Select[Flatten[Table[FromDigits/@Tuples[{6,7,9},n],{n,5}]],PrimeQ] (* Harvey P. Dale, Jun 18 2021 *)

A385770 Primes having only {0, 6, 7} as digits.

Original entry on oeis.org

7, 67, 607, 677, 6007, 6067, 6607, 7607, 60077, 60607, 66067, 67607, 67777, 70067, 70607, 70667, 76607, 76667, 76777, 606077, 606607, 607007, 607067, 607667, 660067, 660607, 666067, 666607, 666667, 666707, 670777, 676007, 677077, 677767, 700067

Offset: 1

Jason Bard, Jul 09 2025

			6007 is a term because it is prime and has only {0,6,7} as digits.

Subsequence of A030432.

Cf. A000040, A020469, A385776.

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

Select[FromDigits/@Tuples[{0,6,7},5],PrimeQ]

primes_with(, 1, [0, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("067"), 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

A385794 Primes having only {4, 6, 7} as digits.

Original entry on oeis.org

7, 47, 67, 467, 647, 677, 4447, 7477, 44647, 44777, 46447, 46477, 46747, 47777, 64667, 64747, 66467, 67447, 67477, 67777, 74747, 76667, 76777, 77447, 77477, 77647, 77747, 444677, 444767, 446447, 446477, 446647, 446767, 447467, 447677, 464447, 464467, 464647, 464747

Offset: 1

Jason Bard, Jul 13 2025

Subsequence of A030432.
Supersequence of A020465, A020469.
Cf. A000040, A385776.

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

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

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

print(list(islice(primes_with("467"), 41))) # uses function/imports in A385776

A385799 Primes having only {6, 7, 8} as digits.

Original entry on oeis.org

7, 67, 677, 787, 877, 887, 7687, 7867, 7877, 8677, 8867, 8887, 66877, 67777, 67867, 68687, 68767, 68777, 76667, 76777, 77687, 77867, 78787, 78877, 78887, 86677, 86767, 87767, 87877, 87887, 88667, 88867, 666667, 667687, 667867, 668677, 668687, 668867, 677687, 677767

Offset: 1

Jason Bard, Jul 14 2025

Subsequence of A030432, A106111.
Supersequence of A020469, A020470.
Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{6, 7, 8}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [6, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("678"), 41))) # uses function/imports in A385776

A036322 Composite numbers whose prime factors contain no digits other than 6 and 7.

Original entry on oeis.org

49, 343, 469, 2401, 3283, 4489, 4739, 16807, 22981, 31423, 33173, 45359, 117649, 160867, 219961, 232211, 300763, 317513, 458329, 474439, 536669, 537439, 823543, 1126069, 1539727, 1625477, 2105341, 2222591, 3039053, 3208303, 3321073

Offset: 1

Patrick De Geest, Dec 15 1998

The multiplicative closure of A020469 consists of itself, 1, and this sequence. - Charles R Greathouse IV, Jun 25 2014

David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for sequences related to prime factors.

Cf. A020469, A036302-A036325.

Sum_{n>=1} 1/a(n) = Product_{p in A020469} (p/(p - 1)) - Sum_{p in A020469} 1/p - 1 = 0.0268448443... . - Amiram Eldar, May 22 2022

A036948 Smallest n-digit prime containing only the digits 6 and 7, or 0 if no such prime exists.

Original entry on oeis.org

7, 67, 677, 0, 67777, 666667, 6676667, 66666667, 666666667, 6666666767, 66666666667, 666666676667, 6666666667777, 66666667677767, 666666666667777, 6666666666767777, 66666666666667667, 666666666666676667

Offset: 1

Patrick De Geest, Jan 04 1999

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

Cf. A020469, A036229, A036322.

Table[SelectFirst[10#+7&/@FromDigits/@Tuples[{6,7},n],PrimeQ],{n,0,17}]/. (Missing["NotFound"]->0) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 08 2019 *)

cp's OEIS Frontend

A260380 Primes having only {3, 6, 7} as digits.

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A260829 Primes having only {5, 6, 7} as digits.

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A260891 Primes having only {1, 6, 7} as digits.

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Magma

Mathematica

A261184 Primes having only {6, 7, 9} as digits.

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Magma

Mathematica

A385770 Primes having only {0, 6, 7} as digits.

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

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Mathematica

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A385794 Primes having only {4, 6, 7} as digits.

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Magma

Mathematica

PARI

Python

A385799 Primes having only {6, 7, 8} as digits.

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