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.

Previous Showing 11-16 of 16 results.

A284971 Numbers with digits 4 and 7 only.

Original entry on oeis.org

4, 7, 44, 47, 74, 77, 444, 447, 474, 477, 744, 747, 774, 777, 4444, 4447, 4474, 4477, 4744, 4747, 4774, 4777, 7444, 7447, 7474, 7477, 7744, 7747, 7774, 7777, 44444, 44447, 44474, 44477, 44744, 44747, 44774, 44777, 47444, 47447, 47474, 47477, 47744, 47747
Offset: 1

Views

Author

Jaroslav Krizek, Apr 07 2017

Keywords

Crossrefs

Prime terms are in A020465.
Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), this sequence (k = 7), A284972 (k = 8), A284973 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 7}]
  • Mathematica
    Flatten@ Table[FromDigits /@ Tuples[{4, 7}, n], {n, 5}] (* Giovanni Resta, Apr 08 2017 *)
  • PARI
    is(n) = my(x=Set([4, 7]), y=Set([0, 1, 2, 3, 5, 6, 8, 9])); if(#setintersect(Set(digits(n)), x) > 0 && #setintersect(Set(digits(n)), y)==0, return(1)); 0 \\ Felix Fröhlich, Apr 08 2017
  • Python
    def a(n):
  b = bin(n+1)[3:]
  return int("".join(b.replace("0", "4").replace("1", "7")))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Apr 07 2021

A284381 Numbers k with digits 5 and 8 only.

Original entry on oeis.org

5, 8, 55, 58, 85, 88, 555, 558, 585, 588, 855, 858, 885, 888, 5555, 5558, 5585, 5588, 5855, 5858, 5885, 5888, 8555, 8558, 8585, 8588, 8855, 8858, 8885, 8888, 55555, 55558, 55585, 55588, 55855, 55858, 55885, 55888, 58555, 58558, 58585, 58588, 58855, 58858
Offset: 1

Views

Author

Jaroslav Krizek, Mar 28 2017

Keywords

Comments

All terms except the first are composite.

Links

Crossrefs

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), this sequence (k = 8), A284382 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 8}];
  • Mathematica
    Join @@ ((FromDigits /@ Tuples[{5, 8}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)
  • Python
    def a(n): return int(bin(n+1)[3:].replace('0', '5').replace('1', '8'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 08 2021

Formula

a(n) = (A284380(n)+A284382(n))/2. - Robert Israel, Mar 28 2017

A284382 Numbers k with digits 5 and 9 only.

Original entry on oeis.org

5, 9, 55, 59, 95, 99, 555, 559, 595, 599, 955, 959, 995, 999, 5555, 5559, 5595, 5599, 5955, 5959, 5995, 5999, 9555, 9559, 9595, 9599, 9955, 9959, 9995, 9999, 55555, 55559, 55595, 55599, 55955, 55959, 55995, 55999, 59555, 59559, 59595, 59599, 59955, 59959
Offset: 1

Views

Author

Jaroslav Krizek, Mar 28 2017

Keywords

Comments

Prime terms are in A020468.

Links

Crossrefs

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), A284381 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 9}];
  • Mathematica
    Join @@ ((FromDigits /@ Tuples[{5, 9}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)
  • Python
    def a(n): return int(bin(n+1)[3:].replace('0', '5').replace('1', '9'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 09 2021

A284973 Numbers with digits 4 and 9 only.

Original entry on oeis.org

4, 9, 44, 49, 94, 99, 444, 449, 494, 499, 944, 949, 994, 999, 4444, 4449, 4494, 4499, 4944, 4949, 4994, 4999, 9444, 9449, 9494, 9499, 9944, 9949, 9994, 9999, 44444, 44449, 44494, 44499, 44944, 44949, 44994, 44999, 49444, 49449, 49494, 49499, 49944, 49949
Offset: 1

Views

Author

Jaroslav Krizek, Apr 07 2017

Keywords

Crossrefs

Prime terms are in A020466.
Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), A284971 (k = 7), A284972 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 9}]
  • PARI
    a(n,{p=[4,9]})={my(v=binary(n+1));fromdigits(vector(#v-1,i,p[2]*v[i+1]+p[1]*!v[i+1]))} \\ R. J. Cano, Apr 09 2017

A284972 Numbers with digits 4 and 8 only.

Original entry on oeis.org

4, 8, 44, 48, 84, 88, 444, 448, 484, 488, 844, 848, 884, 888, 4444, 4448, 4484, 4488, 4844, 4848, 4884, 4888, 8444, 8448, 8484, 8488, 8844, 8848, 8884, 8888, 44444, 44448, 44484, 44488, 44844, 44848, 44884, 44888, 48444, 48448, 48484, 48488, 48844, 48848
Offset: 1

Views

Author

Jaroslav Krizek, Apr 07 2017

Keywords

Comments

All terms are even.

Crossrefs

Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), A284971 (k = 7), this sequence (k = 8), A284973 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 8}]
  • Mathematica
    Flatten@ Table[FromDigits /@ Tuples[{4, 8}, n], {n, 5}] (* Giovanni Resta, Apr 07 2017 *)
  • PARI
    a(n) = my (b = binary(1+n)); b[1] = 0; return (4*(10^(#b-1)-1)/(10-1) + (8-4)*fromdigits(b)) \\ Rémy Sigrist, Apr 08 2017
  • PARI
    a(n)={my(v=binary(n+1));v[1]=0;v+=vector(#v,i,i>1);4*fromdigits(v)} \\ R. J. Cano, Apr 08 2017
  • PARI
    a(n,{p=[4,8]})={my(v=binary(n+1));fromdigits(vector(#v-1,i,p[2]*v[i+1]+p[1]*!v[i+1]))} \\ R. J. Cano, Apr 09 2017

Formula

a(n) = 2 * A284920(n) = 4 * A032822(n).

A359925 Numbers with easy multiplication table - the first 9 multiples of these numbers can be derived by either incrementing or decrementing the corresponding digits from the previous multiple.

Original entry on oeis.org

1, 9, 11, 89, 91, 109, 111, 889, 891, 909, 911, 1089, 1091, 1109, 1111, 8889, 8891, 8909, 8911, 9089, 9091, 9109, 9111, 10889, 10891, 10909, 10911, 11089, 11091, 11109, 11111, 88889, 88891, 88909, 88911, 89089, 89091, 89109, 89111, 90889, 90891, 90909, 90911
Offset: 1

Views

Author

Kiran Ananthpur Bacche, Jan 25 2023

Keywords

Comments

This is also the list of numbers having exactly one dot or one antidot in each box in the Decimal Exploding Dots notation.

Examples

			a(4) = 89. The first nine multiples of 89 are {089, 178, 267, 356, 445, 534, 623, 712, 801}. The digits in the hundreds place increment by 1, while the digits in the tens and units place decrement by 1. In the Decimal Exploding Dots notation, 89 is represented as DOT-ANTIDOT-ANTIDOT = 100 - 10 - 1 = 89

Links

Crossrefs

Cf. A006257, A147991, A147992, A153777, A147993, A256290.
Column k=10 of A360099.

Programs

  • Maple
    a:= proc(n) option remember;
      `if`(n=0, 0, 10*a(iquo(n, 2, 'm'))+2*m-1)
    end:
seq(a(n), n=1..44);   # Alois P. Heinz, Jan 25 2023

Formula

a(n) = 10*a(floor(n/2))+2*(n mod 2)-1 for n>0, a(0)=0. - Alois P. Heinz, Jan 25 2023
a(n) = 2*A256290(n-1) + 1 for n>1. - Hugo Pfoertner, Jan 28 2023
Previous Showing 11-16 of 16 results.

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

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