A020456 -id:A020456 - cp's OEIS frontend

A260270 Primes having only {1, 4, 8} as digits.

11, 41, 181, 811, 881, 1181, 1481, 1811, 4111, 4441, 4481, 8111, 11411, 14411, 18181, 18481, 41141, 41411, 44111, 48481, 81181, 84181, 84481, 84811, 88411, 88811, 118411, 141181, 141481, 141811, 144481, 148411, 181141, 184111, 184181, 184441, 411841, 418181

Offset: 1

Vincenzo Librandi, Jul 23 2015

A020452 and A020456 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. similar sequences listed in A260266.

Cf. A020452, A020456.

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

Select[Prime[Range[4 10^4]], Complement[IntegerDigits[#], {1, 4, 8}]=={} &]
Table[Select[10#+1&/@(FromDigits/@Tuples[{1,4,8},n]),PrimeQ],{n,5}]// Flatten (* Harvey P. Dale, Jun 08 2019 *)

A260892 Primes having only {1, 7, 8} as digits.

Original entry on oeis.org

7, 11, 17, 71, 181, 787, 811, 877, 881, 887, 1117, 1171, 1181, 1187, 1777, 1787, 1811, 1871, 1877, 7177, 7187, 7717, 7817, 7877, 8111, 8117, 8171, 8887, 11117, 11171, 11177, 11717, 11777, 11887, 17117, 17881, 18181, 18787, 71171, 71711, 71777, 71881, 71887

Offset: 1

Vincenzo Librandi, Aug 07 2015

A020455, A020456 and A020470 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, A020455, A020456, A020470.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1, 7, 8]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {1, 7, 8}] == {} &]

A385780 Primes having only {1, 5, 8} as digits.

Original entry on oeis.org

5, 11, 151, 181, 811, 881, 1151, 1181, 1511, 1811, 5581, 5851, 5881, 8111, 8581, 11551, 15511, 15551, 15581, 15881, 18181, 51151, 51511, 51551, 51581, 55511, 58111, 58151, 58511, 81181, 81551, 88811, 111581, 115151, 115811, 155581, 155851, 158551, 158581

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020453, A020456.

Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{1, 5, 8}, n], PrimeQ], {n, 7}]]

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

print(list(islice(primes_with("158"), 41))) # uses function/imports in A385776

A385782 Primes having only {1, 6, 8} as digits.

Original entry on oeis.org

11, 61, 181, 661, 811, 881, 1181, 1811, 1861, 6661, 8111, 8161, 8681, 8861, 11161, 11681, 16111, 16661, 16811, 18181, 18661, 61681, 61861, 66161, 68111, 68161, 68611, 68881, 81181, 81611, 86111, 86161, 86861, 88661, 88681, 88811, 88861, 111611, 116681, 116881

Offset: 1

Jason Bard, Jul 13 2025

Subsequence of A030430. Supersequence of A020454, A020456.

Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{1, 6, 8}, n], PrimeQ], {n, 7}]]
Select[10Flatten[Table[FromDigits/@Tuples[{1,6,8},n],{n,5}]]+1,PrimeQ] (* Harvey P. Dale, Aug 27 2025 *)

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

print(list(islice(primes_with("168"), 41))) # uses function/imports in A385776

A385783 Primes having only {1, 8, 9} as digits.

Original entry on oeis.org

11, 19, 89, 181, 191, 199, 811, 881, 911, 919, 991, 1181, 1811, 1889, 1999, 8111, 8191, 8819, 8999, 9181, 9199, 9811, 11119, 11981, 18119, 18181, 18191, 18199, 18899, 18911, 18919, 19181, 19819, 19889, 19891, 19919, 19991, 81119, 81181, 81199, 81899, 81919

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020456, A020457, A020472.

Cf. A000040, A385776.

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

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

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

print(list(islice(primes_with("189"), 41))) # uses function/imports in A385776

A385775 Primes having only {1, 2, 8} as digits.

Original entry on oeis.org

2, 11, 181, 211, 281, 811, 821, 881, 1181, 1811, 2111, 2221, 2281, 8111, 8221, 8821, 11821, 12211, 12281, 12821, 18121, 18181, 18211, 21121, 21211, 21221, 21821, 21881, 22111, 22811, 28111, 28181, 28211, 81181, 81281, 82811, 88211, 88811, 111121

Offset: 1

Jason Bard, Jul 09 2025

Supersequence of A020450, A020456.

Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{1, 2, 8}, n], PrimeQ], {n, 7}]]

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

print(list(islice(primes_with("128"), 41))) # uses function/imports in A385776

A385778 Primes having only {1, 3, 8} as digits.

Original entry on oeis.org

3, 11, 13, 31, 83, 113, 131, 181, 311, 313, 331, 383, 811, 881, 883, 1181, 1381, 1811, 1831, 3181, 3313, 3331, 3833, 3881, 8111, 8311, 8831, 11113, 11131, 11311, 11383, 11813, 11831, 11833, 13183, 13313, 13331, 13381, 13831, 13883, 18131, 18133, 18181, 18311

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020451, A020456, A020464.

Cf. A000040, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{1, 3, 8}, n], PrimeQ], {n, 7}]]

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

print(list(islice(primes_with("138"), 41))) # uses function/imports in A385776

A213084 Numbers consisting of ones and eights.

Original entry on oeis.org

1, 8, 11, 18, 81, 88, 111, 118, 181, 188, 811, 818, 881, 888, 1111, 1118, 1181, 1188, 1811, 1818, 1881, 1888, 8111, 8118, 8181, 8188, 8811, 8818, 8881, 8888, 11111, 11118, 11181, 11188, 11811, 11818, 11881, 11888, 18111, 18118, 18181, 18188, 18811, 18818

Offset: 1

Jens Ahlström, Jun 05 2012

One and eight begin with vowels. The subsequence of primes begins 11, 181, 811, 1181, 1811, 8111. - Jonathan Vos Post, Jun 14 2012

Alois P. Heinz, Table of n, a(n) for n = 1..16382

Cf. A020456 (primes in this sequence).

Cf. numbers consisting of 1s and ks: A007088 (k=0), A007931 (k=2), A032917 (k=3), A032822 (k=4), A276037 (k=5), A284293 (k=6), A276039 (k=7), A284294 (k=9).

Flatten[Table[FromDigits/@Tuples[{1,8},n],{n,5}]] (* Harvey P. Dale, Aug 27 2014 *)

is(n) = #setintersect(vecsort(digits(n), , 8), [0, 2, 3, 4, 5, 6, 7, 9])==0 \\ Felix Fröhlich, Sep 09 2019

res = []
i = 0
while len (res) < 260:
    for c in str(i):
        if c in '18':
            continue
        else:
            break
    else:
        res.append(i)
    i = i + 1
print(res)

def a(n): return int(bin(n+1)[3:].replace('1', '8').replace('0', '1'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jun 26 2025

A036308 Composite numbers whose prime factors contain no digits other than 1 and 8.

Original entry on oeis.org

121, 1331, 1991, 8921, 9691, 12991, 14641, 19921, 21901, 32761, 89221, 98131, 106601, 142901, 146791, 159461, 161051, 199991, 213761, 219131, 240911, 327791, 360371, 657721, 714491, 776161, 892991, 957791, 976921, 981431, 1040461, 1079441, 1172611, 1394761, 1468091

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020456. - David A. Corneth, Oct 09 2020

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 58 terms from Vincenzo Librandi)
Index entries for sequences related to prime factors.

Cf. A020456, A036302-A036325.

[n: n in [4..1500000] | not IsPrime(n) and forall{f: f in PrimeDivisors(n) | Intseq(f) subset [1,8]}]; // Bruno Berselli, Aug 26 2013

dpfQ[n_]:=Module[{d=Union[Flatten[IntegerDigits/@Transpose[FactorInteger[n]][[1]]]]}, !PrimeQ[n]&&(d == {1}||d == {8}||d == {1, 8})]; Select[Range[2, 1500000], dpfQ] (* Vincenzo Librandi, Aug 25 2013 *)

Sum_{n>=1} 1/a(n) = Product_{p in A020456} (p/(p - 1)) - Sum_{p in A020456} 1/p - 1 = 0.0101097220... . - Amiram Eldar, May 18 2022

More terms from Vincenzo Librandi, Aug 25 2013

A036935 Smallest n-digit prime containing only digits 1 and 8, or 0 if no such prime exists.

Original entry on oeis.org

0, 11, 181, 1181, 18181, 0, 1111181, 11818181, 111111181, 1111111181, 11111188811, 0, 1111111118111, 11111111818181, 111111111111881, 1111111111111181, 11111111111188111, 0, 1111111111111111111

Offset: 1

Patrick De Geest, Jan 04 1999

a(6k) = 0 as any 6k-digit number containing only digits 1 or 8 is divisible by 7. - Jinyuan Wang, Mar 09 2020

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

Cf. A020456, A036229, A036308.

cp's OEIS Frontend

A260270 Primes having only {1, 4, 8} as digits.

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A260892 Primes having only {1, 7, 8} as digits.

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A385780 Primes having only {1, 5, 8} as digits.

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A385782 Primes having only {1, 6, 8} as digits.

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A385783 Primes having only {1, 8, 9} as digits.

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A385775 Primes having only {1, 2, 8} as digits.

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A385778 Primes having only {1, 3, 8} as digits.

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A213084 Numbers consisting of ones and eights.

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