A132291 Base 10 strong Skolem-Langford numbers.

12132003, 23121300, 30023121, 31213200, 1214230043, 1312432004, 2342131400, 2412134003, 3004312142, 3400324121, 4002342131, 4131243200, 1213267345006475, 1213275364005746, 1214267540036573, 1214273645300765, 1214275640035763, 1215247365430076

Offset: 1

Author

Eric Angelini, Jun 26 2005, Aug 10 2007

Keywords

• base
• easy
• fini
• full
• nonn

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.

"Strong" means that every digit from 0 to the largest digit of a(n) must be present in a(n). See A108116 for the "weak" variant without this additional constraint.

Number of digits of a(n) == 0 or 2 (mod 8)

Largest element is a(2820) = 867315136875420024.

Links

• D. Wilson, Complete table of n, a(n) for n = 1..2820

Crossrefs

Base 10 Skolem-Langford numbers are in A108116.

Base 10 weaker Skolem-Langford numbers are in A357826.

Programs

Python

def A132291gen(): # SL() is in A108116
  for numd in range(1, 11):
    dset = ("0123456789")[:numd]
    s = [0 for _ in range(2*numd)]
    for an in sorted(SL(dset, s)):
      yield an
for n, an in enumerate(A132291gen(), start=1):
  print(n, an) # Michael S. Branicky, Dec 14 2020

Extensions

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