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.

A284380 Numbers k with digits 5 and 7 only.

Original entry on oeis.org

5, 7, 55, 57, 75, 77, 555, 557, 575, 577, 755, 757, 775, 777, 5555, 5557, 5575, 5577, 5755, 5757, 5775, 5777, 7555, 7557, 7575, 7577, 7755, 7757, 7775, 7777, 55555, 55557, 55575, 55577, 55755, 55757, 55775, 55777, 57555, 57557, 57575, 57577, 57755, 57757
Offset: 1

Views

Author

Jaroslav Krizek, Mar 28 2017

Keywords

Links

Crossrefs

Prime terms are in A020467.
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), this sequence (k = 7), A284381 (k = 8), A284382 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 7}];
  • Mathematica
    Join @@ ((FromDigits /@ Tuples[{5, 7}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)
  • Python
    from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
  n, digits, alst = 0, 1, []
  while len(alst) < terms:
    mpstr = "".join(d*digits for d in "57")
    for mp in multiset_permutations(mpstr, digits):
      alst.append(int("".join(mp)))
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(44)) # Michael S. Branicky, May 07 2021

A004092 Sum of digits of even numbers.

Original entry on oeis.org

0, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 3, 5, 7, 9, 11, 4, 6, 8, 10, 12, 5, 7, 9, 11, 13, 6, 8, 10, 12, 14, 7, 9, 11, 13, 15, 8, 10, 12, 14, 16, 9, 11, 13, 15, 17, 1, 3, 5
Offset: 0

Views

Author

N. J. A. Sloane, Dec 11 1996

Keywords

Comments

a(n) >= A007953(n) / 5 with equality iff n is in A169964 (see Diophante link). - Bernard Schott, Apr 29 2023

Links

Crossrefs

Cf. A007953, A169964.

Programs

Formula

a(n) = 2n - 9*Sum_{k=1..1+floor(log_10(2n))} floor( n/(5*10^(k-1)) ). - Anthony Browne, Jun 18 2016
a(n) = A007953(2n). - Alois P. Heinz, Apr 11 2018

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

A078244 Smallest multiple of n using only digits 0 and 5.

Original entry on oeis.org

5, 50, 555, 500, 5, 5550, 5005, 5000, 555555555, 50, 55, 55500, 5005, 50050, 555, 50000, 55505, 5555555550, 55005, 500, 50505, 550, 550505, 555000, 50, 50050, 5505555555, 500500, 5505505, 5550, 555055, 500000, 555555, 555050, 5005
Offset: 1

Views

Author

Amarnath Murthy, Nov 23 2002

Keywords

Comments

a(n) = min{A169964(k): k > 1 and A169964(k) mod n = 0}. [Reinhard Zumkeller, Jan 10 2012]

Links

Crossrefs

Cf. A004290, A078241-A078248, A079339, A096681-A096688.

Programs

  • Haskell
    a078244 n = head [x | x <- tail a169964_list, mod x n == 0]
-- Reinhard Zumkeller, Jan 10 2012
  • Mathematica
    Module[{mlts=Rest[FromDigits/@Tuples[{0,5},12]]},Table[ SelectFirst[ mlts,Divisible[ #,n]&],{n,40}]] (* Harvey P. Dale, Aug 14 2021 *)

Extensions

More terms from Ray Chandler, Jul 12 2004

A343810 Numbers that contain only the digits 0,4,8. Permutable multiples of 4: numbers k such that every permutation of the digits of k is a multiple of 4.

Original entry on oeis.org

0, 4, 8, 40, 44, 48, 80, 84, 88, 400, 404, 408, 440, 444, 448, 480, 484, 488, 800, 804, 808, 840, 844, 848, 880, 884, 888, 4000, 4004, 4008, 4040, 4044, 4048, 4080, 4084, 4088, 4400, 4404, 4408, 4440, 4444, 4448, 4480, 4484, 4488, 4800, 4804
Offset: 0

Views

Author

Ctibor O. Zizka, Apr 30 2021

Keywords

Comments

Also permutable multiples of 4: numbers k such that every permutation of the digits of k is a multiple of 4.

Examples

			480 = 4*120, 408 = 4*102, 840 = 4*210, 804 = 4*201, 048 = 4*12, 084 = 4*21.

Crossrefs

Cf. A003459, A007089, A008585, A008586, A014263, A061811, A169964.

Programs

  • Maple
    f:= proc(n) local L,i;
  L:= convert(n,base,3);
  4*add(L[i]*10^(i-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, Apr 30 2021
  • Mathematica
    FromDigits /@ Tuples[{0, 4, 8}, 4] (* Amiram Eldar, Apr 30 2021 *)
  • PARI
    a(n) = fromdigits(digits(n, 3))*4 \\ Rémy Sigrist, May 05 2021

Formula

a(n) = 4*A007089(n).
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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