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

1,2

Comments

The sequence is finite. Last term: 999999999888888887777777666666555554444333221.

Number of terms is 66712890763701234740813164553708284. - Zak Seidov, Jan 02 2007

Fixed points of A139337. - Reinhard Zumkeller, Apr 14 2008

Sequence contains squares (A181392) and cubes (A225886^3) but no higher powers, see Comments in A181392. - Giovanni Resta, May 19 2013

Links

T. D. Noe, Table of n, a(n) for n=1..21056 (terms < 10^10)

Michael S. Branicky, Python program

Example

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.

Prog

(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

Crossrefs

Cf. A127007, A139337, A078348 (subsequence of primes), A181392, A225886.

Sequence in context: A156293 A225308 A043498 * A247700 A105776 A044354

Adjacent sequences: A108568 A108569 A108570 * A108572 A108573 A108574

Keyword

base,easy,fini,nonn

Author

Eric Angelini, Jul 05 2005

Status

approved