A020472 -id:A020472 - cp's OEIS frontend

A199348 Primes having only {3, 4, 8} as digits.

3, 43, 83, 383, 433, 443, 883, 3343, 3433, 3833, 4483, 8443, 33343, 34483, 34843, 34883, 38333, 38833, 44383, 44483, 44843, 48383, 48883, 83383, 83443, 83833, 83843, 84443, 88843, 88883, 333383, 333433, 334333, 334843, 338383, 343333, 343433, 344483, 344843, 348433, 348443, 348833, 348883, 383483, 383833, 384343, 384383, 388483

Offset: 1

M. F. Hasler, Nov 05 2011

All terms end in 3 and those > 3 never have the same number of 4's and 8's.

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A020449 - A020472, A199325 - A199329, A385768 - A385800.

Table[Select[FromDigits/@Tuples[{3,4,8},n],PrimeQ],{n,6}]//Flatten (* Harvey P. Dale, Apr 09 2022 *)

a(n, list=0, L=[3, 4, 8], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u) || next; reqpal & !isprime(A004086(t)) & next; list & print1(t", "); n--||return(t)))}

A284069 Numbers whose smallest decimal digit is 8.

Original entry on oeis.org

8, 88, 89, 98, 888, 889, 898, 899, 988, 989, 998, 8888, 8889, 8898, 8899, 8988, 8989, 8998, 8999, 9888, 9889, 9898, 9899, 9988, 9989, 9998, 88888, 88889, 88898, 88899, 88988, 88989, 88998, 88999, 89888, 89889, 89898, 89899, 89988, 89989, 89998, 89999, 98888

Offset: 1

Jaroslav Krizek, Mar 24 2017

Numbers n such that A054054(n) = 8.

Prime terms are in A020472. - Corrected by Robert Israel, Apr 05 2017

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), A284064 (k = 3), A284065 (k = 4), A284066 (k = 5), A284067 (k = 6), A284068 (k = 7), this sequence (k = 8), A002283 (k = 9).

Cf. A020472, A054054.

[n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 8]

F:= proc(d) local r; # to get all terms with d digits
r:= 8*(10^d-1)/9;
op(sort(convert(map(t -> r + add(10^(j-1),j=t), combinat:-powerset(d) minus {{$1..d}}),list)))
end proc:
map(F, [$1..5]); # Robert Israel, Apr 05 2017

Flatten@ Table[ Most[ FromDigits /@ Tuples[{8,9}, k]], {k,5}] (* Giovanni Resta, Mar 24 2017 *)

isok(n) = vecmin(digits(n)) == 8; \\ Michel Marcus, Mar 25 2017

print([n for n in range(8, 10**6) if min(str(n))=='8']) # Indranil Ghosh, Apr 06 2017

From Robert Israel, Apr 05 2017: (Start)
a(2*j+2^(m+1)-m-3) = 10*a(j+2^m-m-1)+8 for j=1..2^m-1.
a(2*j+2^(m+1)-m-2) = 10*a(j+2^m-m-1)+9 for j=1..2^m-1.
a(2^(m+1)-m-2) = 10^m-2. (End)

A199326 Primes having only {0, 1, 6} as digits.

Original entry on oeis.org

11, 61, 101, 601, 661, 1061, 1601, 6011, 6101, 6661, 10061, 10111, 10601, 11161, 16001, 16061, 16111, 16661, 60101, 60161, 60601, 60611, 60661, 61001, 66161, 66601, 101111, 101161, 101611, 106661, 110161, 111611, 116101, 160001, 161611, 166601, 600011, 600101, 600601, 601061, 610661, 611011, 611101, 611111

Offset: 1

M. F. Hasler, Nov 05 2011

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

Cf. A020449 - A020472, A199325 - A199329, A061247.

Select[FromDigits/@Tuples[{0,1,6},6],PrimeQ] (* Harvey P. Dale, Dec 25 2018 *)

{L=[0,1,6];for(d=1,6,u=vector(d,i,10^(d-i))~;forvec(v=vector(d,i,[1+(i==1 & !L[1]),#L]),ispseudoprime(t=vector(d,i,L[v[i]])*u)&print1(t",")))} /* see A199327 for a function a() */

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

A385790 Primes having only {2, 8, 9} as digits.

Original entry on oeis.org

2, 29, 89, 229, 829, 929, 2999, 8929, 8999, 9829, 9929, 22229, 28229, 28289, 29989, 82889, 88289, 89899, 89989, 92899, 98299, 98899, 98929, 98999, 99289, 99829, 99929, 99989, 222289, 228299, 228829, 228929, 228989, 282229, 282299, 282889, 288929, 288989, 289889

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020460, A020472.

Cf. A000040, A030433, A385776.

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

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

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

print(list(islice(primes_with("289"), 41))) # uses function/imports in A385776

A385792 Primes having only {3, 8, 9} as digits.

Original entry on oeis.org

3, 83, 89, 383, 389, 839, 883, 983, 3389, 3833, 3889, 3989, 8389, 8839, 8893, 8933, 8999, 9833, 9839, 9883, 33889, 33893, 38333, 38393, 38833, 38839, 38933, 38993, 39383, 39839, 39883, 39983, 39989, 83339, 83383, 83389, 83399, 83833, 83933, 83939, 83983, 88339

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020464, A020472.

Cf. A000040, A385776.

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

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

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

print(list(islice(primes_with("389"), 41))) # uses function/imports in A385776

A385798 Primes having only {5, 8, 9} as digits.

Original entry on oeis.org

5, 59, 89, 599, 859, 8599, 8999, 9859, 55589, 55889, 58889, 59999, 85889, 85999, 88589, 89599, 89899, 89959, 89989, 95959, 95989, 98899, 98999, 99559, 99859, 99989, 555589, 558599, 559859, 585889, 585899, 585989, 589859, 598999, 599899, 599959, 599999, 855889

Offset: 1

Jason Bard, Jul 14 2025

Supersequence of A020468, A020472.

Cf. A000040, A030433, A385776.

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

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

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

print(list(islice(primes_with("589"), 41))) # uses function/imports in A385776

A385796 Primes having only {4, 8, 9} as digits.

Original entry on oeis.org

89, 449, 499, 4889, 4999, 8849, 8999, 9949, 44449, 48449, 48889, 48989, 49499, 49999, 84449, 84499, 88499, 89449, 89849, 89899, 89989, 94849, 94889, 94949, 94999, 98849, 98899, 98999, 99989, 444449, 448999, 449989, 484489, 484999, 489449, 489989, 494849, 494899

Offset: 1

Jason Bard, Jul 13 2025

Subsequence of A030433.
Supersequence of A020466, A020472.
Cf. A000040, A385776.

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

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

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

print(list(islice(primes_with("489"), 41))) # uses function/imports in A385776

A099651 For each of the C(10,2) = 45 pairs of decimal digits, record the smallest prime containing only these digits (if one exists); sort.

Original entry on oeis.org

13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 59, 61, 67, 79, 83, 89, 101, 151, 181, 211, 227, 449, 557, 787

Offset: 1

Labos Elemer, Nov 11 2004

The sequence consists of 24 terms, of which 16 cases < 100.

From 45 combinations of 10 decimal digits only 24 can be prime. All least cases are here.

			Primes with digits of 8 and 9 are in A020472:{89,8999,89899,89989..}. The smallest = 89 is here.
The 24 digit pairs sorted least to greatest that can be prime are {01, 12, 13, 14, 15, 16, 17, 18, 19, 23, 27, 29, 34, 35, 37, 38, 47, 49, 57, 59, 67, 78, 79, 89}. - _Michael De Vlieger_, Mar 02 2017

Cf. A020449-A020472, A099756.

Sort@ Map[Module[{k = 1}, While[! SameQ[Union@ IntegerDigits@ Prime@ k, #], k++]; Prime@ k] &, Function[r, {{0, 1}}~Join~DeleteCases[Union@ Map[Sort, Tuples[Range@ 9, 2]], w_ /; Or[Times @@ Boole@ Map[EvenQ, w] > 0, SameQ @@ w, Times @@ Boole@ Map[Mod[#, 3] == 0 &, w] > 0, SubsetQ[r, w], w == {5, 6}]]]@ Select[Range[2, 9], PowerMod[10, #, #] == 0 &]] (* Michael De Vlieger, Mar 02 2017 *)

A385772 Primes having only {0, 8, 9} as digits.

Original entry on oeis.org

89, 809, 8009, 8089, 8999, 80809, 80909, 80989, 89009, 89809, 89899, 89909, 89989, 90089, 90989, 98009, 98809, 98899, 98909, 98999, 99089, 99809, 99989, 800089, 800909, 800999, 809909, 880909, 888809, 888989, 889909, 890809, 890999, 898889, 899009, 900089

Offset: 1

Jason Bard, Jul 09 2025

			8999 is a term because it is prime and has only {0,8,9} as digits.

Subsequence of A030433.

Cf. A000040, A020472, A385776.

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

Select[FromDigits/@Tuples[{0,8,9},5],PrimeQ]

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

print(list(islice(primes_with("089"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A199348 Primes having only {3, 4, 8} as digits.

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A284069 Numbers whose smallest decimal digit is 8.

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A199326 Primes having only {0, 1, 6} as digits.

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

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A385790 Primes having only {2, 8, 9} as digits.

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A385792 Primes having only {3, 8, 9} as digits.

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A385798 Primes having only {5, 8, 9} as digits.

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A385796 Primes having only {4, 8, 9} as digits.

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