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 1-4 of 4 results.

A112516 Numbers k such that the first 9 decimal digits of the k-th Fibonacci number is 1-9 pandigital.

Original entry on oeis.org

2749, 4589, 7102, 7727, 8198, 9383, 12633, 15708, 19014, 21206, 21303, 21434, 21566, 22706, 22890, 25790, 28244, 29877, 32174, 32717, 34433, 34883, 37965, 44691, 47422, 48635, 54473, 60438, 60536, 63902, 68340, 72424, 73147, 75873
Offset: 1

Views

Author

Roger Hui, Dec 22 2005

Keywords

Examples

			The 2749th Fibonacci number is:
14372 68955 33879 17661 82964 56715 64334 14434 76345 06448 91772 ...
which is 1-9 pandigital in its first 9 digits.

Crossrefs

Cf. A000045, A112371.

Programs

  • J
    NB. (www.jsoftware.com):
plus=: 4 : 0
'x xe'=. +. x.
'y ye'=. +. y.
e=. xe>.ye
z=. (x*10^xe-e)+y*10^ye-e
(z%10^b) j. e+b=. 10<:z
)
g =: 3 : '{."1 ({:,plus/)^:(
  • Maple
    filter:= n -> convert(convert(combinat:-fibonacci(n),base,10)[-9..-1],set) = {$1..9}:
select(filter, [$40.. 5 * 10^4]); # Robert Israel, May 31 2015
  • Mathematica
    fQ[n_] := Sort@Take[IntegerDigits@Fibonacci@n, 9] == {1, 2, 3, 4, 5, 6, 7, 8, 9}; Select[ Range[40, 77705], fQ[ # ] &] (* Robert G. Wilson v, Dec 27 2005 *)

Extensions

a(31)-a(34) from Robert G. Wilson v, Dec 27 2005

A140532 Number of primes with n distinct decimal digits, none of which are 0.

Original entry on oeis.org

4, 20, 83, 395, 1610, 5045, 12850, 23082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Norman Morton (mathtutorer(AT)yahoo.com), Jul 03 2008

Keywords

Comments

a(9) is zero because 1+2+...+9 = 45 which is divisible by 3, making any number with 9 distinct digits also divisible by 3. - Wei Zhou, Oct 02 2011
The maximal distinct-digit prime without 0's is 98765431. Thus, a(n) = 0 for n >= 9. - Michael S. Branicky, Apr 20 2021

Examples

			a(1) = #{2,3,5,7} = 4.
a(2) = #{13,17,19,23,...,97} = 20. Note that the prime 11 is omitted because its decimal digits are not distinct.

Crossrefs

Cf. A112371, A073532.

Programs

  • Mathematica
    Length /@ Table[Select[FromDigits /@ Permutations[Range@9, {i}], PrimeQ], {i,9}] (* Wei Zhou, Oct 02 2011 *)
  • Python
    from itertools import permutations
from sympy import isprime, primerange
def distinct_digs(n): s = str(n); return len(s) == len(set(s))
def a(n):
  if n >= 9: return 0
  return sum(isprime(int("".join(p))) for p in permutations("123456789", n))
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Apr 20 2021

Extensions

Corrected by Charles R Greathouse IV, Aug 02 2010

A216488 Numbers k such that the last 9 digits of the k-th Lucas number are 1-9 pandigital.

Original entry on oeis.org

3352, 3837, 7239, 18503, 19344, 22628, 29363, 30994, 37514, 47058, 48201, 50371, 51702, 51857, 53586, 55469, 56248, 56668, 60560, 65206, 70610, 72171, 76554, 78310, 78380, 82628, 82952, 82993, 93615, 99751, 101179, 104469, 105347, 105379, 106327, 113251, 114970, 116751, 117313
Offset: 1

Views

Author

V. Raman, Sep 07 2012

Keywords

Links

Crossrefs

Cf. A000032.
Cf. A112516 for Fibonacci numbers such that first 9 digits are 1-9 pandigital.
Cf. A112371 for Fibonacci numbers such that last 9 digits are 1-9 pandigital.

Programs

  • Maple
    b:= proc(n) b(n):= `if`(n<2, 2-n, irem(b(n-1)+b(n-2), 10^9)) end:
q:= n-> is({convert(b(n), base, 10)[]}={$1..9}):
select(q, [$1..120000])[];  # Alois P. Heinz, Jul 04 2021
  • Mathematica
    Select[Range[39, 120000], Sort[Take[IntegerDigits[LucasL[#]], -9]] == {1, 2, 3, 4, 5, 6, 7, 8, 9} &] (* Tanya Khovanova, Jul 04 2021 *)
  • Python
    def afind(limit):
    bkm1, bk = 2, 1
    for k in range(2, limit+1):
        bkm1, bk = bk, bkm1 + bk
        if set(str(bk)[-9:]) == set("123456789"): print(k, end=", ")
afind(10**6) # Michael S. Branicky, Jul 04 2021

A216489 Numbers k such that the first 9 digits of the k-th Lucas number are 1-9 pandigital.

Original entry on oeis.org

10524, 10960, 11199, 15957, 16247, 17734, 20187, 29879, 30046, 31998, 38874, 40181, 44757, 47078, 47773, 48101, 49125, 50674, 50717, 51607, 54399, 57943, 59563, 64305, 64453, 68160, 76227, 77624, 84268, 86070, 89792, 91069, 91496, 92481, 95472, 97418, 97698, 98390, 99021
Offset: 1

Views

Author

V. Raman, Sep 07 2012

Keywords

Links

Crossrefs

Cf. A112516 for Fibonacci numbers such that first 9 digits are 1-9 pandigital.
Cf. A112371 for Fibonacci numbers such that last 9 digits are 1-9 pandigital.
Showing 1-4 of 4 results.

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