A108571 Any digit d in the sequence says: "I am part of an integer in which you'll find d digits d".
1, 22, 122, 212, 221, 333, 1333, 3133, 3313, 3331, 4444, 14444, 22333, 23233, 23323, 23332, 32233, 32323, 32332, 33223, 33232, 33322, 41444, 44144, 44414, 44441, 55555, 122333, 123233, 123323, 123332, 132233, 132323, 132332, 133223, 133232, 133322, 155555
Offset: 1
Examples
23323 is in the sequence because it has two 2's and three 3's. 23332 is in the sequence because it has two 2's and three 3's. 23333 is not in the sequence because it has only one 2 and four 3's.
Links
- T. D. Noe, Table of n, a(n) for n=1..21056 (terms < 10^10)
- Michael S. Branicky, Python program
Programs
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PARI
is(n)={ vecmin(n=vecsort(digits(n))) && #n==normlp(Set(n),1) && !for(i=1,#n, n[i+n[i]-1]==n[i] || return; i+n[i]>#n || n[i+n[i]]>n[i] || return; n[i]>1 && i+=n[i]-1)} \\ M. F. Hasler, Sep 22 2014 -
Python
# see link for a function that directly generates terms def ok(n): s = str(n); return all(s.count(d) == int(d) for d in set(s)) def aupto(limit): return [m for m in range(1, limit+1) if ok(m)] print(aupto(155555)) # Michael S. Branicky, Jan 22 2021
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