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 11 results. Next

A260269 Primes having only {1, 4, 6} as digits.

Original entry on oeis.org

11, 41, 61, 461, 641, 661, 4111, 4441, 6661, 11161, 11411, 14411, 14461, 16111, 16141, 16411, 16661, 41141, 41161, 41411, 41611, 41641, 44111, 44641, 46141, 46411, 46441, 61141, 61441, 64661, 66161, 111611, 111641, 114161, 114641, 114661, 116141, 116411
Offset: 1

Views

Author

Vincenzo Librandi, Jul 23 2015

Keywords

Comments

A020452 and A020454 are subsequences.

Links

Crossrefs

Cf. similar sequences listed in A260266.
Cf. A020452, A020454.

Programs

  • Magma
    [p: p in PrimesUpTo(4*10^5) | Set(Intseq(p)) subset [1, 4, 6]];
  • Mathematica
    Select[Prime[Range[3 10^4]], Complement[IntegerDigits[#], {1, 4, 6}]=={} &]

A260891 Primes having only {1, 6, 7} as digits.

Original entry on oeis.org

7, 11, 17, 61, 67, 71, 167, 617, 661, 677, 761, 1117, 1171, 1667, 1777, 6661, 6761, 7177, 7717, 11117, 11161, 11171, 11177, 11617, 11677, 11717, 11777, 16111, 16661, 17117, 17167, 17761, 61667, 61717, 66161, 66617, 67777, 71161, 71167, 71171, 71671
Offset: 1

Views

Author

Vincenzo Librandi, Aug 05 2015

Keywords

Comments

A020454, A020455 and A020469 are subsequences.

Links

Crossrefs

Cf, similar sequences listed in A260889.
Cf. A000040, A020454, A020455, A020469.

Programs

  • Magma
    [p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1, 6, 7]];
  • Mathematica
    Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 6, 7}] == {} &]

A284293 Numbers using only digits 1 and 6.

Original entry on oeis.org

1, 6, 11, 16, 61, 66, 111, 116, 161, 166, 611, 616, 661, 666, 1111, 1116, 1161, 1166, 1611, 1616, 1661, 1666, 6111, 6116, 6161, 6166, 6611, 6616, 6661, 6666, 11111, 11116, 11161, 11166, 11611, 11616, 11661, 11666, 16111, 16116, 16161, 16166, 16611, 16616
Offset: 1

Views

Author

Jaroslav Krizek, Mar 25 2017

Keywords

Comments

Product of digits of n is a power of 6; subsequence of A276038.
Prime terms are in A020454.

Links

Crossrefs

Cf. Numbers using only digits 1 and k for k = 0 and k = 2 - 9: A007088 (k = 0), A007931 (k = 2), A032917 (k = 3), A032822 (k = 4) , A276037 (k = 5), this sequence (k = 6), A276039 (k = 7), A213084 (k = 8), A284294 (k = 9).

Programs

  • Magma
    [n: n in [1..20000] | Set(IntegerToSequence(n, 10)) subset {1, 6}];
  • Mathematica
    Join @@ (FromDigits /@ Tuples[{1,6}, #] & /@ Range[5]) (* Giovanni Resta, Mar 25 2017 *)
  • Python
    def A284293(n): return 5*int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1)//9 # Chai Wah Wu, Jun 28 2025

A385779 Primes having only {1, 5, 6} as digits.

Original entry on oeis.org

5, 11, 61, 151, 661, 1151, 1511, 5651, 6151, 6551, 6661, 11161, 11551, 15161, 15511, 15551, 15661, 16111, 16561, 16651, 16661, 51151, 51511, 51551, 55511, 55661, 56611, 61151, 61511, 61561, 61651, 65111, 65551, 65651, 66161, 111611, 115151, 115561, 151561
Offset: 1

Views

Author

Jason Bard, Jul 13 2025

Keywords

Links

Crossrefs

Supersequence of A020453, A020454.
Cf. A000040, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 5, 6]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{1, 5, 6}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(, 1, [1, 5, 6]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("156"), 41))) # uses function/imports in A385776

A363023 Primes having only {1, 6, 9} as digits.

Original entry on oeis.org

11, 19, 61, 191, 199, 619, 661, 691, 911, 919, 991, 1619, 1669, 1699, 1999, 6199, 6619, 6661, 6691, 6911, 6961, 6991, 9161, 9199, 9619, 9661, 11119, 11161, 11699, 11969, 16111, 16619, 16661, 16691, 16699, 19661, 19699, 19919, 19961, 19991, 61169, 61961
Offset: 1

Views

Author

Harvey P. Dale, May 13 2023

Keywords

Links

Crossrefs

Cf. A020454 (1 and 6), A020457 (1 and 9).
Cf. A385776.

Programs

  • Mathematica
    Table[Select[Flatten[10#+{1,9}&/@FromDigits/@Tuples[{1,6,9},n]],PrimeQ],{n,4}]//Flatten

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

Views

Author

Jason Bard, Jul 13 2025

Keywords

Links

Crossrefs

Subsequence of A030430. Supersequence of A020454, A020456.
Cf. A000040, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 6, 8]];
  • Mathematica
    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 *)
  • PARI
    primes_with(, 1, [1, 6, 8]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("168"), 41))) # uses function/imports in A385776

A385774 Primes having only {1, 2, 6} as digits.

Original entry on oeis.org

2, 11, 61, 211, 661, 1621, 2111, 2161, 2221, 2621, 6121, 6211, 6221, 6661, 11161, 11261, 11621, 12161, 12211, 12611, 16111, 16661, 21121, 21211, 21221, 21611, 21661, 22111, 22621, 26111, 26161, 26261, 61121, 61211, 61261, 66161, 66221, 111121, 111211
Offset: 1

Views

Author

Jason Bard, Jul 09 2025

Keywords

Links

Crossrefs

Supersequence of A020450, A020454.
Cf. A000040, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 2, 6]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{1, 2, 6}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(, 1, [1, 2, 6]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("126"), 41))) # uses function/imports in A385776

A385777 Primes having only {1, 3, 6} as digits.

Original entry on oeis.org

3, 11, 13, 31, 61, 113, 131, 163, 311, 313, 331, 613, 631, 661, 1163, 1361, 1613, 1663, 3163, 3313, 3331, 3361, 3613, 3631, 6113, 6131, 6133, 6163, 6311, 6361, 6661, 11113, 11131, 11161, 11311, 11633, 13163, 13313, 13331, 13613, 13633, 16111
Offset: 1

Views

Author

Jason Bard, Jul 09 2025

Keywords

Links

Crossrefs

Supersequence of A020451, A020454.
Cf. A000040, A385776.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 3, 6]];
  • Mathematica
    Flatten[Table[Select[FromDigits /@ Tuples[{1, 3, 6}, n], PrimeQ], {n, 7}]]
  • PARI
    primes_with(,1,[1,3,6]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("136"), 41))) # uses function/imports in A385776

A036306 Composite numbers whose prime factors contain no digits other than 1 and 6.

Original entry on oeis.org

121, 671, 1331, 3721, 7271, 7381, 14641, 40321, 40931, 73271, 79981, 81191, 122771, 161051, 177221, 183271, 226981, 406321, 436921, 443531, 450241, 680821, 727771, 805981, 879791, 893101, 982771, 1016321, 1227721, 1350481, 1771561
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020454. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A020454, A036302-A036325.

Programs

  • Mathematica
    pf16Q[n_]:=Module[{pfs=Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[1]]]]},pfs=={1}||pfs=={1,6}]; Select[Range[ 2*10^6],CompositeQ[#]&&pf16Q[#]&] (* Harvey P. Dale, Jul 12 2014 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020454} (p/(p - 1)) - Sum_{p in A020454} 1/p - 1 = 0.0112607346... . - Amiram Eldar, May 18 2022

A036933 Smallest n-digit prime containing only digits 1 and 6, or 0 if no such prime exists.

Original entry on oeis.org

0, 11, 661, 6661, 11161, 111611, 1111661, 11111161, 111616111, 1111161661, 11111111611, 111111111611, 1111111111661, 11111111616611, 111111111116111, 1111111111616161, 11111111111611661, 111111111111111161
Offset: 1

Views

Author

Patrick De Geest, Jan 04 1999

Keywords

Links

Crossrefs

Cf. A020454, A036229, A036306.

Programs

  • Mathematica
    Join[{0},Flatten[Table[Select[Sort[FromDigits/@Tuples[{1,6},i]], PrimeQ, 1], {i,2,20}]]] (* Harvey P. Dale, May 06 2014 *)
Showing 1-10 of 11 results. Next

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