A188531 Numbers which contain only the digit 4 in their base-5 representation, with at most one exception. If the exception is the most-significant digit, it must be the digit 1, 2, or 3, otherwise the exception must be the digit 3.

1, 2, 3, 4, 9, 14, 19, 23, 24, 49, 74, 99, 119, 123, 124, 249, 374, 499, 599, 619, 623, 624, 1249, 1874, 2499, 2999, 3099, 3119, 3123, 3124, 6249, 9374, 12499, 14999, 15499, 15599, 15619, 15623, 15624, 31249, 46874, 62499, 74999, 77499, 77999, 78099, 78119

Offset: 1

Author

Vladimir Shevelev, Apr 03 2011

Keywords

• nonn
• base

Comments

The sequence lists the positive binomial coefficient predictors in base 5. For definition, see paper in link.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• V. Shevelev, Binomial Coefficient Predictors, Journal of Integer Sequences, Vol. 14 (2011), Article 11.2.8.

Crossrefs

Cf. A089633, A188341, A188499, A188529.

Programs

Maple

a:= proc(n) option remember; local i, l, m, t;
      m:= `if`(n=1, 0, a(n-1));
      l:=NULL;
      for t while m>0 do l:=l, irem(m, 5, 'm') od;
      l:= array([l, 0]);
      for i while l[i]=4 do od;
      if l[i]<3 then l[i]:= l[i]+1
                else l[i]:= 4;
                     if i>1 then l[i-1]:= 3 fi
      fi;
      add(l[i] *5^(i-1), i=1..t)
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 03 2011

Mathematica

aQ[n_] := Module[{d=IntegerDigits[n,5]}, s=Select[d, #!=4 &]; s=={} || s =={3} || (d[[1]]<3 && s=={d[[1]]})]; Select[Range[100000], aQ] (* Amiram Eldar, Dec 14 2018 *)

PARI

listb(nd) = {for (i = 1, nd, my(v = vector(nd, k, 4), kstart = if (i==1, 1, 3)); for (k=kstart,3, v[i] = k; print1(fromdigits(v, 5), ", "););); print1(fromdigits(vector(nd, k, 4), 5), ", ");}
lista(nnd) = {for (nd=1, nnd, listb(nd););} \\ Michel Marcus, Dec 14 2018