A106110 -id:A106110 - cp's OEIS frontend

A261181 Primes that contain only the digits (0, 7, 9).

7, 79, 97, 709, 797, 907, 977, 997, 7079, 7907, 9007, 9907, 70009, 70079, 70099, 70709, 70979, 70997, 70999, 77797, 77977, 77999, 79777, 79907, 79979, 79997, 79999, 90007, 90709, 90907, 90977, 90997, 97007, 97777, 99079, 99707, 99709, 99907, 700079

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020471 is a subsequence.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)

Cf. Primes that contain only the digits (k,7,9): this sequence (k=0), A260893 (k=1), A261182 (k=2), A260382 (k=3), A261183 (k=4), A260831 (k=5), A261184 (k=6), A106110 (k=8).

Cf. A000040, A020471.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [0, 7, 9]];

Select[Prime[Range[6 10^4]], Complement[IntegerDigits[#], {0, 7, 9}] == {} &]
Select[FromDigits/@Tuples[{0,7,9},6],PrimeQ] (* Harvey P. Dale, Aug 09 2024 *)

A106112 Primes with minimal digit > 4.

Original entry on oeis.org

5, 7, 59, 67, 79, 89, 97, 557, 569, 577, 587, 599, 659, 677, 757, 769, 787, 797, 857, 859, 877, 887, 967, 977, 997, 5557, 5569, 5657, 5659, 5669, 5689, 5779, 5857, 5867, 5869, 5879, 5897, 5987, 6569, 6577, 6599, 6659, 6679, 6689, 6779, 6857, 6869, 6899, 6959

Offset: 1

Zak Seidov, May 07 2005

Jason Bard, Table of n, a(n) for n = 1..10000

Cf. A036956 (primes with maximal digit <= 4).

Cf. A106110, A106111, A106114, A106115.

Select[Prime[Range[1000]], Min[IntegerDigits[ # ]]>4&]

A154523 Numbers k such that the smallest decimal digit of k equals the smallest decimal digit of prime(k).

Original entry on oeis.org

11, 13, 18, 31, 41, 52, 62, 73, 80, 81, 110, 112, 113, 114, 115, 116, 121, 125, 128, 133, 135, 140, 141, 142, 152, 156, 157, 164, 167, 170, 180, 187, 188, 189, 191, 192, 193, 194, 195, 196, 198, 199, 211, 215, 216, 217, 218, 219, 221, 231, 241, 251, 261, 271

Offset: 1

Juri-Stepan Gerasimov, Jan 11 2009

Natural density 1, since almost all numbers and almost all primes (thanks to the prime number theorem) contain the digit 0.

The first terms with smallest digit 1, 2, and 3 are listed in the Data section. The first with smallest digits 4, 5, and 6 are 644, 758, and 6666, respectively. While there are plenty of primes with no decimal digit smaller than 7 (see A106110), including many primes consisting only of the digits 8 and 9 (the 10th of which is prime(77777) = 989999; cf. A020472), it seems to me that finding a term in this sequence whose smallest digit is 7 or 8 should be a very difficult problem. - Jon E. Schoenfield, Feb 11 2019

			11 is a term because prime(11) =  31 (smallest digits: 1);
13 is a term because prime(13) =  41 (smallest digits: 1);
18 is a term because prime(18) =  61 (smallest digits: 1);
31 is a term because prime(31) = 127 (smallest digits: 1);
41 is a term because prime(41) = 179 (smallest digits: 1);
52 is a term because prime(52) = 239 (smallest digits: 2).

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

Cf. A020472, A106110.

A054054 := proc(n) min(op(convert(n,base,10)) ) ; end proc:
for n from 1 to 500 do if A054054(n) = A054054(ithprime(n)) then printf("%d,",n ) ; end if; end do: (End) # R. J. Mathar, May 05 2010

Transpose[Select[Table[{n,Prime[n]},{n,300}],Min[IntegerDigits[#[[1]]]] == Min[IntegerDigits[#[[2]]]]&]][[1]] (* Harvey P. Dale, Dec 18 2012 *)

Corrected (221 inserted) by R. J. Mathar, May 05 2010

Definition clarified by Harvey P. Dale, Dec 18 2012

A386084 Primes having only {0, 7, 8, 9} as digits.

Original entry on oeis.org

7, 79, 89, 97, 709, 787, 797, 809, 877, 887, 907, 977, 997, 7079, 7789, 7877, 7879, 7907, 8009, 8087, 8089, 8707, 8779, 8807, 8887, 8999, 9007, 9787, 9887, 9907, 70009, 70079, 70099, 70709, 70877, 70879, 70979, 70997, 70999, 77797, 77899, 77977, 77999, 78007

Offset: 1

Jason Bard, Jul 16 2025

Supersequence of A106110, A261181, A385771, A385772.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 7, 8, 9]];

Select[FromDigits /@ Tuples[{0, 7, 8, 9}, n], PrimeQ]

primes_with(, 1, [0, 7, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("0789"), 41))) # uses function/imports in A385776

A386138 Primes having only {1, 7, 8, 9} as digits.

Original entry on oeis.org

7, 11, 17, 19, 71, 79, 89, 97, 179, 181, 191, 197, 199, 719, 787, 797, 811, 877, 881, 887, 911, 919, 971, 977, 991, 997, 1117, 1171, 1181, 1187, 1777, 1787, 1789, 1811, 1871, 1877, 1879, 1889, 1979, 1987, 1997, 1999, 7177, 7187, 7717, 7789, 7817, 7877, 7879, 7919

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A106110, A260892, A260893, A385783.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 7, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 7, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 7, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("1789"), 41))) # uses function/imports in A385776

A386168 Primes having only {2, 7, 8, 9} as digits.

Original entry on oeis.org

2, 7, 29, 79, 89, 97, 227, 229, 277, 727, 787, 797, 827, 829, 877, 887, 929, 977, 997, 2287, 2297, 2729, 2777, 2789, 2797, 2879, 2887, 2897, 2927, 2999, 7229, 7297, 7727, 7789, 7829, 7877, 7879, 7927, 8287, 8297, 8779, 8887, 8929, 8999, 9227, 9277, 9787, 9829

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A106110, A261182, A385789, A385790.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 7, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 7, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 7, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("2789"), 41))) # uses function/imports in A385776

A386187 Primes having only {3, 7, 8, 9} as digits.

Original entry on oeis.org

3, 7, 37, 73, 79, 83, 89, 97, 337, 373, 379, 383, 389, 397, 733, 739, 773, 787, 797, 839, 877, 883, 887, 937, 977, 983, 997, 3373, 3389, 3733, 3739, 3779, 3793, 3797, 3833, 3877, 3889, 3989, 7333, 7393, 7789, 7793, 7873, 7877, 7879, 7883, 7933, 7937, 7993, 8377

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A106110, A260381, A260382, A385792.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [3, 7, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{3, 7, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [3, 7, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("3789"), 41))) # uses function/imports in A385776

A386195 Primes having only {4, 7, 8, 9} as digits.

Original entry on oeis.org

7, 47, 79, 89, 97, 449, 479, 487, 499, 787, 797, 877, 887, 947, 977, 997, 4447, 4787, 4789, 4799, 4877, 4889, 4987, 4999, 7477, 7487, 7489, 7499, 7789, 7877, 7879, 7949, 8447, 8747, 8779, 8849, 8887, 8999, 9479, 9497, 9749, 9787, 9887, 9949, 44449, 44497, 44777

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A106110, A261183, A385795, A385796.

Cf. A000040, A051416, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 7, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 7, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 7, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("4789"), 41))) # uses function/imports in A385776

A386199 Primes having only {5, 7, 8, 9} as digits.

Original entry on oeis.org

5, 7, 59, 79, 89, 97, 557, 577, 587, 599, 757, 787, 797, 857, 859, 877, 887, 977, 997, 5557, 5779, 5857, 5879, 5897, 5987, 7559, 7577, 7589, 7757, 7759, 7789, 7877, 7879, 8597, 8599, 8779, 8887, 8999, 9587, 9787, 9857, 9859, 9887, 55579, 55589, 55787, 55799, 55889

Offset: 1

Jason Bard, Jul 18 2025

Supersequence of A106110, A260830, A260831, A385798.

Cf. A000040, A106111, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [5, 7, 8, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{5, 7, 8, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [5, 7, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("5789"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A261181 Primes that contain only the digits (0, 7, 9).

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Magma

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A106112 Primes with minimal digit > 4.

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A154523 Numbers k such that the smallest decimal digit of k equals the smallest decimal digit of prime(k).

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A386084 Primes having only {0, 7, 8, 9} as digits.

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Magma

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A386138 Primes having only {1, 7, 8, 9} as digits.

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Magma

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A386168 Primes having only {2, 7, 8, 9} as digits.

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Magma

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A386187 Primes having only {3, 7, 8, 9} as digits.

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Magma

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A386195 Primes having only {4, 7, 8, 9} as digits.

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