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] &]

A317407 The "OOPS" numbers -- numbers with ones in all odd-numbered positions of the binary representation of n.

Original entry on oeis.org

1, 2, 3, 5, 7, 10, 11, 14, 15, 21, 23, 29, 31, 42, 43, 46, 47, 58, 59, 62, 63, 85, 87, 93, 95, 117, 119, 125, 127, 170, 171, 174, 175, 186, 187, 190, 191, 234, 235, 238, 239, 250, 251, 254, 255, 341, 343, 349, 351, 373, 375, 381, 383, 469, 471, 477, 479, 501
Offset: 1

Views

Author

Jeffrey Shallit, Jul 28 2018

Keywords

Comments

Here we number positions starting with the most significant digit as position 1, and continue to the right down to the least significant digit.
From David A. Corneth, Jul 29 2018: (Start)
1 is in the sequence.
If k is in the sequence then so is 2k+1.
(End)
If A070939(k) is odd and k is in the sequence then so is 2*k. - Robert Israel, Jul 31 2018

Examples

			23 is in the sequence because its binary representation is 10111, and it has ones in positions 1,3,5.

Links

Crossrefs

Cf. A032911, A070939.

Programs

  • Maple
    S[1]:= [1]:
for n from 2 to 10 do
  if n::odd then S[n]:= map(t -> 2*t+1, S[n-1])
  else S[n]:= map(t -> (2*t,2*t+1),S[n-1])
  fi
od;
map(op,[seq(S[i],i=1..10)]); # Robert Israel, Jul 31 2018
  • PARI
    isok(n) = {my(b=binary(n)); forstep (i=1, #b, 2, if (!b[i], return (0));); return (1);} \\ Michel Marcus, Jul 29 2018

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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