A215876 Numbers that contain each decimal digit at least twice.

10012233445566778899, 10012233445566778989, 10012233445566778998, 10012233445566779889, 10012233445566779898, 10012233445566779988, 10012233445566787899, 10012233445566787989, 10012233445566787998, 10012233445566788799

Offset: 1

Author

M. F. Hasler, Aug 25 2012

Keywords

• nonn
• base
• look

Comments

A subsequence of A171102. Contains A000079 o A215830, i.e., { 2^A215830(n); n=1,2,3... }, as a subsequence.

The first 17!/2^8 ~ 1.4e12 terms are of the form 10^19 + x, where x runs over all permutations of the digits 12233445566788799, up to 99887766554433221.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

nextp:= proc(L) local m, i,j, r, rj;
for m from 2 while L[m-1] <= L[m] do od:
r:= 10:
for j from 1 to m-1 do
   if L[j] > L[m] and L[j] < r then
      r:= L[j]; rj:= j;
   fi
od;
[ op(sort([seq(L[i],i={$1..m} minus {rj})],`>`)), r,seq(L[i],i=m+1..nops(L))]
end proc:
A[1]:= 10012233445566778899:
L:= convert(A[1],base,10):
for n from 2 to 100 do
  L:= nextp(L);
  A[n]:= add(L[i]*10^(i-1),i=1..nops(L));
od:
seq(A[i],i=1..100); # Robert Israel, Feb 25 2019

PARI

is_A215876(N)={my(c=vector(10)); for(k=1,#N=Vecsmall(Str(N)), c[N[k]-47]++); vecmin(c)>1}