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A108116 Base 10 weak Skolem-Langford numbers. 5
2002, 131003, 231213, 300131, 312132, 420024, 12132003, 14130043, 15120025, 23121300, 23421314, 25121005, 25320035, 30023121, 31213200, 31413004, 34003141, 40031413, 41312432, 45001415, 45121425, 45300435, 50012152, 51410054, 52002151, 52412154, 53002352, 53400354, 61310036 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Self-describing numbers: between two digits "d" there are d digits.

a(n) has either 0 or 2 instances of any digit, hence even number of digits.

Largest element is a(20120) = 978416154798652002.

Named after the Norwegian mathematician Thoralf Albert Skolem (1887-1963) and the British chemist and mathematics teacher Charles Dudley Langford (1905-1969). - Amiram Eldar, Jun 17 2021

REFERENCES

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

LINKS

D. Wilson, Complete table of n, a(n) for n = 1..20120

EXAMPLE

In "2002" there are 2 digits between the two 2's and 0 digits between the two 0's.

In "131003" there is 1 digit between the two 1's, 3 digits between the two 3's and 0 digit between the two 0's.

PROG

(Python)

def SL(d, s):

  for i1 in range(int(d[0]=="0"), len(s)-int(d[0])-1):

    i2 = i1 + int(d[0]) + 1

    if not (s[i1] or s[i2]):

      s[i1] = s[i2] = d[0]

      r = d[1:]

      if r: yield from SL(r, s)

      else: yield int("".join(s))

      s[i1] = s[i2] = 0

from itertools import chain, combinations as C

def A108116gen():

  for numd in range(1, 11):

    dset, s = "0123456789", [0 for _ in range(2*numd)]

    for an in sorted(

      chain.from_iterable(SL("".join(c), s) for c in C(dset, numd))):

      yield an

for n, an in enumerate(A108116gen(), start=1):

  print(n, an) # Michael S. Branicky, Dec 14 2020

CROSSREFS

Base 10 strong Skolem-Langford numbers are in A132291.

Sequence in context: A250880 A154049 A339803 * A140920 A162240 A127351

Adjacent sequences:  A108113 A108114 A108115 * A108117 A108118 A108119

KEYWORD

base,easy,fini,full,nonn

AUTHOR

Eric Angelini, Jun 26 2005, Aug 10 2007

EXTENSIONS

Edited by N. J. A. Sloane, Nov 18 2007

STATUS

approved

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Last modified July 29 11:53 EDT 2021. Contains 346346 sequences. (Running on oeis4.)