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 1-3 of 3 results.

A351894 Numbers that contain only odd digits in their factorial-base representation.

Original entry on oeis.org

1, 3, 9, 21, 33, 45, 81, 93, 153, 165, 201, 213, 393, 405, 441, 453, 633, 645, 681, 693, 873, 885, 921, 933, 1113, 1125, 1161, 1173, 1353, 1365, 1401, 1413, 2313, 2325, 2361, 2373, 2553, 2565, 2601, 2613, 2793, 2805, 2841, 2853, 3753, 3765, 3801, 3813, 3993, 4005
Offset: 1

Views

Author

Amiram Eldar, Feb 24 2022

Keywords

Comments

All the terms above 1 are odd multiples of 3.

Examples

			3 is a term since its factorial-base presentation, 11, has only odd digits.
21 is a term since its factorial-base presentation, 311, has only odd digits.

Links

Crossrefs

Cf. A007623, A016945, A351893.
Subsequence: A007489
Similar sequences: A003462 \ {0} (ternary), A014261 (decimal), A032911 (base 4), A032912 (base 5), A033032 (base 6), A033033 (base 7), A033034 (base 8), A033035 (base 9), A033036 (base 11), A033037 (base 12), A033038 (base 13), A033039 (base 14), A033040 (base 15), A033041 (base 16), A126646 (binary).

Programs

  • Mathematica
    max = 7; fctBaseDigits[n_] := IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; Select[Range[1, max!, 2], AllTrue[fctBaseDigits[#], OddQ] &]

A212495 Numbers all of whose base 11 digits are even.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 22, 24, 26, 28, 30, 32, 44, 46, 48, 50, 52, 54, 66, 68, 70, 72, 74, 76, 88, 90, 92, 94, 96, 98, 110, 112, 114, 116, 118, 120, 242, 244, 246, 248, 250, 252, 264, 266, 268, 270, 272, 274, 286, 288, 290, 292, 294, 296, 308, 310, 312, 314, 316
Offset: 1

Views

Author

Douglas Latimer, May 18 2012

Keywords

Comments

Similar in definition to A033036.
As n increases, it is most likely that A212495(n) < A033036(n), although exceptions to this rule can be found. I conjecture that A212495(n) > A033036(n) for only finitely many values of n.

Examples

			30 is represented by "28" in base 11. Both digits in this representation are even, thus 30 belongs to the sequence.

Programs

  • Mathematica
    Select[Range[0,350],AllTrue[IntegerDigits[#,11],EvenQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 03 2018 *)
  • PARI
    {is(c) = local(d);while(c != 0, d=c%11; c=(c-d)/11; if(d%2==1, return(0))) ; 1}
for(i=0, 317, if(is(i), print1(i, ", ")))

A363242 Numbers whose primorial-base representation contains only odd digits.

Original entry on oeis.org

1, 3, 9, 21, 39, 51, 99, 111, 159, 171, 249, 261, 309, 321, 369, 381, 669, 681, 729, 741, 789, 801, 1089, 1101, 1149, 1161, 1209, 1221, 1509, 1521, 1569, 1581, 1629, 1641, 1929, 1941, 1989, 2001, 2049, 2061, 2559, 2571, 2619, 2631, 2679, 2691, 2979, 2991, 3039
Offset: 1

Views

Author

Amiram Eldar, May 23 2023

Keywords

Comments

All the terms above 1 are odd multiples of 3.
The partial sums of the primorials (A143293) are terms, since the primorial-base representation of A143293(n) is n+1 1's.

Examples

			3 is a term since its primorial-base presentation, 11, has only odd digits.
21 is a term since its primorial-base presentation, 311, has only odd digits.

Links

Crossrefs

Cf. A002110, A049345, A328849.
Subsequence: A143293.
Similar sequences: A003462 \ {0} (ternary), A014261 (decimal), A032911 (base 4), A032912 (base 5), A033032 (base 6), A033033 (base 7), A033034 (base 8), A033035 (base 9), A033036 (base 11), A033037 (base 12), A033038 (base 13), A033039 (base 14), A033040 (base 15), A033041 (base 16), A126646 (binary), A351894 (factorial base).

Programs

  • Mathematica
    With[{max = 5}, bases = Prime@ Range[max, 1, -1]; nmax = Times @@ bases - 1; prmBaseDigits[n_] := IntegerDigits[n, MixedRadix[bases]]; Select[Range[1, nmax, 2], AllTrue[prmBaseDigits[#], OddQ] &]]
  • PARI
    is(n) = {my(p = 2); if(n < 1, return(0)); while(n > 0, if((n%p)%2 == 0, return(0)); n \= p; p = nextprime(p+1)); return(1);}
Showing 1-3 of 3 results.

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

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