cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 13 results. Next

A385776 Primes having only {1, 2, 9} as digits.

Original entry on oeis.org

2, 11, 19, 29, 191, 199, 211, 229, 911, 919, 929, 991, 1129, 1229, 1291, 1999, 2111, 2129, 2221, 2999, 9199, 9221, 9929, 11119, 11299, 12119, 12211, 12911, 12919, 19121, 19211, 19219, 19919, 19991, 21121, 21191, 21211, 21221, 21911, 21929, 21991
Offset: 1

Views

Author

Jason Bard, Jul 09 2025

Keywords

Links

Crossrefs

Supersequence of A020450, A020457, A020460.
Cf. A000040.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 2, 9]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{1, 2, 9}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(n=50, show=0, L=[1, 2, 9])={for(d=1, 1e9, my(t, u=vector(d, i, 10^(d-i))~); forvec(v=vector(d, i, [1+!(L[1]||(i>1&&i
  • Python
    from gmpy2 import is_prime
from itertools import count, islice, product
def primes_with(digits):  # generator of primes having only set(digits) as digits
    S, E = "".join(sorted(set(digits) - {'0'})), "".join(sorted(set(digits) & set("1379")))
    yield from (p for p in [2, 3, 5, 7] if str(p) in digits)
    yield from (t for d in count(2) for s in S for m in product(digits, repeat=d-2) for e in E if is_prime(t:=int(s+"".join(m)+e)))
print(list(islice(primes_with("129"), 41))) # Michael S. Branicky, Jul 11 2025

A260128 Primes having only {2, 3, 9} as digits.

Original entry on oeis.org

2, 3, 23, 29, 223, 229, 233, 239, 293, 929, 2239, 2293, 2333, 2339, 2393, 2399, 2939, 2999, 3229, 3299, 3323, 3329, 3923, 3929, 9239, 9293, 9323, 9923, 9929, 22229, 22993, 23293, 23333, 23339, 23399, 23929, 23993, 29333, 29339, 29399, 32233, 32299, 32323
Offset: 1

Views

Author

Vincenzo Librandi, Jul 17 2015

Keywords

Comments

A020458 and A020460 are subsequences.

Links

Crossrefs

Cf. similar sequences listed in A260125.
Cf. A020458, A020460.

Programs

  • Magma
    [p: p in PrimesUpTo(300000) | Set(Intseq(p)) subset [2, 3, 9]];
  • Mathematica
    Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {2, 3, 9}]=={} &]
Select[FromDigits/@Flatten[Table[Tuples[{2,3,9},n],{n,5}],1],PrimeQ] (* Harvey P. Dale, Apr 15 2025 *)

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

Views

Author

Vincenzo Librandi, Aug 11 2015

Keywords

Comments

A020459, A020460 and A020471 are subsequences.

Links

Crossrefs

Cf. similar sequences listed in A261181.
Cf. A000040, A020459, A020460, A020471, A385776.

Programs

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

A385785 Primes having only {2, 4, 9} as digits.

Original entry on oeis.org

2, 29, 229, 449, 499, 929, 2999, 4229, 4999, 9929, 9949, 22229, 24229, 24499, 29429, 42299, 42499, 42929, 44249, 44449, 49429, 49499, 49999, 94229, 94949, 94999, 99929, 222499, 224299, 224429, 224449, 224929, 229249, 229499, 229949, 242449, 242999, 244429
Offset: 1

Views

Author

Jason Bard, Jul 13 2025

Keywords

Links

Crossrefs

Supersequence of A020460, A020466.
Cf. A000040, A030433, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 4, 9]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{2, 4, 9}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(, 1, [2, 4, 9]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("249"), 41))) # uses function/imports in A385776

A385786 Primes having only {2, 5, 9} as digits.

Original entry on oeis.org

2, 5, 29, 59, 229, 599, 929, 2999, 9929, 22229, 22259, 25229, 25999, 29599, 29959, 52259, 52529, 52999, 55229, 55259, 55529, 59929, 59999, 92959, 95929, 95959, 99259, 99529, 99559, 99929, 225299, 225529, 229529, 252559, 255259, 259229, 295259, 522229, 522259
Offset: 1

Views

Author

Jason Bard, Jul 13 2025

Keywords

Links

Crossrefs

Supersequence of A020460, A020468.
Cf. A000040, A030433, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 5, 9]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{2, 5, 9}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(, 1, [2, 5, 9]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("259"), 41))) # uses function/imports in A385776

A385788 Primes having only {2, 6, 9} as digits.

Original entry on oeis.org

2, 29, 229, 269, 929, 2269, 2699, 2969, 2999, 6229, 6269, 6299, 9629, 9929, 22229, 22669, 22699, 26669, 26699, 29269, 29629, 29669, 62299, 62929, 62969, 66629, 69929, 92269, 92669, 92699, 96269, 99929, 222269, 226669, 229699, 266269, 266999, 292969, 296269
Offset: 1

Views

Author

Jason Bard, Jul 13 2025

Keywords

Links

Crossrefs

Supersequence of A020460.
Cf. A000040, A030433, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 6, 9]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{2, 6, 9}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(, 1, [2, 6, 9]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("269"), 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

Views

Author

Jason Bard, Jul 13 2025

Keywords

Links

Crossrefs

Supersequence of A020460, A020472.
Cf. A000040, A030433, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 8, 9]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{2, 8, 9}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(, 1, [2, 8, 9]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("289"), 41))) # uses function/imports in A385776

A261268 Primes having only {0, 2, 9} as digits.

Original entry on oeis.org

2, 29, 229, 929, 2029, 2099, 2909, 2999, 9029, 9209, 9929, 20029, 20929, 22229, 29009, 29209, 92009, 99929, 200009, 200029, 200909, 200929, 202099, 202999, 209029, 209299, 209929, 220009, 222029, 290209, 290999, 292909, 299029, 299099, 299909, 900929
Offset: 1

Views

Author

Vincenzo Librandi, Aug 18 2015

Keywords

Comments

A020460 is a subsequence.

Links

Crossrefs

Cf. similar sequences listed in A261267.
Cf. A000040, A020460.

Programs

  • Magma
    [p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0, 2, 9]];
  • Mathematica
    Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {0, 2, 9}] == {} &]

A284923 Numbers with digits 2 and 9 only.

Original entry on oeis.org

2, 9, 22, 29, 92, 99, 222, 229, 292, 299, 922, 929, 992, 999, 2222, 2229, 2292, 2299, 2922, 2929, 2992, 2999, 9222, 9229, 9292, 9299, 9922, 9929, 9992, 9999, 22222, 22229, 22292, 22299, 22922, 22929, 22992, 22999, 29222, 29229, 29292, 29299, 29922, 29929
Offset: 1

Views

Author

Jaroslav Krizek, Apr 06 2017

Keywords

Crossrefs

Prime terms are in A020460.
Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), A284920 (k = 4), A072961 (k = 5), A284632 (k = 6), A284921 (k = 7), A284922 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 9}]
  • Mathematica
    Select[Range[30000],SubsetQ[{2,9},Sort[DeleteDuplicates[IntegerDigits[#]]]] &] (* Stefano Spezia, Aug 06 2025 *)

A036313 Composite numbers whose prime factors contain no digits other than 2 and 9.

Original entry on oeis.org

4, 8, 16, 32, 58, 64, 116, 128, 232, 256, 458, 464, 512, 841, 916, 928, 1024, 1682, 1832, 1856, 1858, 2048, 3364, 3664, 3712, 3716, 4096, 5998, 6641, 6728, 7328, 7424, 7432, 8192, 11996, 13282, 13456, 14656, 14848, 14864, 16384, 19858, 23992, 24389
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020460. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A020460, A036302-A036325.

Programs

  • Maple
    S[1]:= [2,9]:
for d from 2 to 5 do S[d]:= map(t -> (10*t+2,10*t+9), S[d-1]) od:
P29:= select(isprime, map(op,[seq(S[i],i=1..5)])):
N:= 10^5:
R:= {1}:
for p in P29 do
  R:= map(t -> seq(t*p^j,j=0..floor(log[p](N/t))), R)
od:
R:= R minus convert(P29,set) minus {1}:
sort(convert(R,list)); # Robert Israel, Jan 17 2020
  • Mathematica
    pf29Q[n_]:=Module[{pfs=Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[1]]]]},MatchQ[pfs,{2}]||MatchQ[pfs,{9} ]||MatchQ[pfs,{2,9}]]; nn=25000;Select[Complement[Range[nn],Prime[ Range[ PrimePi[nn]]]],pf29Q] (* Harvey P. Dale, Apr 23 2012 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020460} (p/(p - 1)) - Sum_{p in A020460} 1/p - 1 = 0.5433646773... . - Amiram Eldar, May 18 2022
Showing 1-10 of 13 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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