A020471 -id:A020471 - cp's OEIS frontend

A020472 Primes that contain digits 8 and 9 only.

89, 8999, 89899, 89989, 98899, 98999, 99989, 888989, 898889, 989999, 998989, 8888989, 8889889, 8988989, 8989999, 8998889, 8999899, 9888889, 9889889, 9899999, 9989899, 9999889, 88888999, 88898989, 88989899, 89888989, 89889889, 89898889, 89999999, 98888989

Offset: 1

David W. Wilson

Or, primes with minimal digit 8.

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
Index to entries about primes with digits in a given set

Cf. A020449 (digits 0 & 1), ..., A020471 (digits 7 & 9). - M. F. Hasler, Mar 18 2010

Select[Prime[Range[80000]], Min[IntegerDigits[#]] == 8 &] (* Zak Seidov, May 07 2005 *)
Flatten[Table[Select[FromDigits/@Tuples[{8, 9}, n], PrimeQ], {n, 8}]] (* Vincenzo Librandi, Jul 27 2012 *)

for(nd=1,9, p=vector(nd,i,10^(nd-i))~; forvec(v=vector(nd,i,[8+(i==nd),9]), isprime(v*p) && print1(v*p","))) \\ M. F. Hasler, Mar 18 2010

from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    for d in count(2):
        for first in product("89", repeat=d-1):
            t = int("".join(first) + "9")
            if isprime(t): yield t
print(list(islice(agen(), 30))) # Michael S. Branicky, Nov 15 2022

Edited by N. J. A. Sloane, Jan 26 2008 at the suggestion of Lekraj Beedassy

A260831 Primes having only {5, 7, 9} as digits.

Original entry on oeis.org

5, 7, 59, 79, 97, 557, 577, 599, 757, 797, 977, 997, 5557, 5779, 7559, 7577, 7757, 7759, 55579, 55799, 55997, 57557, 57559, 57977, 59557, 59779, 59797, 59957, 59999, 75557, 75577, 75797, 75979, 75997, 77557, 77797, 77977, 77999, 79559, 79579, 79757, 79777

Offset: 1

Vincenzo Librandi, Aug 03 2015

A020467, A020468 and A020471 are subsequences.

Subsequence of A030096.

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. A000040, A020467, A020468, A020471, A030096.

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

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {5, 7, 9}] == {} &]

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

Original entry on oeis.org

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 *)

A260893 Primes having only {1, 7, 9} as digits.

Original entry on oeis.org

7, 11, 17, 19, 71, 79, 97, 179, 191, 197, 199, 719, 797, 911, 919, 971, 977, 991, 997, 1117, 1171, 1777, 1979, 1997, 1999, 7177, 7717, 7919, 9199, 9719, 9791, 11117, 11119, 11171, 11177, 11197, 11717, 11719, 11777, 11779, 11971, 17117, 17191, 17791, 17911

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020455, A020457 and A020471 are subsequences.

Subsequence of A030096.

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, A020455, A020457, A020471, A030096.

[p: p in PrimesUpTo(3*10^4) | Set(Intseq(p)) subset [1, 7, 9]];

Select[Prime[Range[3 10^3]], Complement[IntegerDigits[#], {1, 7, 9}] == {}&]

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

A260382 Primes having only {3, 7, 9} as digits.

Original entry on oeis.org

3, 7, 37, 73, 79, 97, 337, 373, 379, 397, 733, 739, 773, 797, 937, 977, 997, 3373, 3733, 3739, 3779, 3793, 3797, 7333, 7393, 7793, 7933, 7937, 7993, 9337, 9377, 9397, 9733, 9739, 9973, 33377, 33739, 33773, 33797, 33937, 33997, 37337, 37339, 37379, 37397

Offset: 1

Vincenzo Librandi, Aug 01 2015

A020463 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 A260378.

Cf. A000040, A020463, A020471.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [3,7,9]];

Select[Prime[Range[5*10^3]], Complement[IntegerDigits[#], {3, 7, 9}]=={} &]

A261183 Primes having only {4, 7, 9} as digits.

Original entry on oeis.org

7, 47, 79, 97, 449, 479, 499, 797, 947, 977, 997, 4447, 4799, 4999, 7477, 7499, 7949, 9479, 9497, 9749, 9949, 44449, 44497, 44777, 44797, 47497, 47777, 47779, 47797, 47947, 47977, 49477, 49499, 49747, 49999, 74449, 74747, 74779, 74797, 77447, 77477, 77479

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020465, A020466 and A020471 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..20000
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, A020465, A020466, A020471.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [4, 7, 9]];

Select[Prime[Range[6 10^4]], Complement[IntegerDigits[#], {4, 7, 9}] == {} &]

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 *)

A036324 Composite numbers whose prime factors have no digits other than 7's and 9's.

Original entry on oeis.org

49, 343, 553, 679, 2401, 3871, 4753, 5579, 6241, 6839, 6979, 7663, 9409, 16807, 27097, 33271, 39053, 43687, 47873, 48853, 53641, 62963, 65863, 77183, 77309, 78763, 94769, 96709, 117649, 189679, 232897, 273371, 305809, 335111, 341971

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020471. - David A. Corneth, Oct 09 2020

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 100 terms from Harvey P. Dale)
Index entries for sequences related to prime factors.

Cf. A020471, A036302-A036325.

Select[Range[342000],CompositeQ[#]&&SubsetQ[{7,9},Union[ Flatten[ IntegerDigits/@ FactorInteger[#][[All,1]]]]]&] (* Harvey P. Dale, Aug 01 2019 *)

Sum_{n>=1} 1/a(n) = Product_{p in A020471} (p/(p - 1)) - Sum_{p in A020471} 1/p - 1 = 0.0287747452... . - Amiram Eldar, May 22 2022

Definition clarified by Harvey P. Dale, Aug 01 2019

A386358 Primes without {7, 9} as digits.

Original entry on oeis.org

2, 3, 5, 11, 13, 23, 31, 41, 43, 53, 61, 83, 101, 103, 113, 131, 151, 163, 181, 211, 223, 233, 241, 251, 263, 281, 283, 311, 313, 331, 353, 383, 401, 421, 431, 433, 443, 461, 463, 503, 521, 523, 541, 563, 601, 613, 631, 641, 643, 653, 661, 683, 811, 821, 823

Offset: 1

Jason Bard, Jul 20 2025

Intersection of A038615 and A038617.

Cf. A000040, A020471, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 3, 4, 5, 6, 8]];

Select[Prime[Range[120]], DigitCount[#, 10, 7] == 0 && DigitCount[#, 10, 9] == 0 &]

primes_with(, 1, [0, 1, 2, 3, 4, 5, 6, 8]) \\ uses function in A385776

print(list(islice(primes_with("01234568"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A020472 Primes that contain digits 8 and 9 only.

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A260831 Primes having only {5, 7, 9} as digits.

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

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A260893 Primes having only {1, 7, 9} as digits.

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

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A260382 Primes having only {3, 7, 9} as digits.

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A261183 Primes having only {4, 7, 9} as digits.

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

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