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

1,2

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.

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 *)

Prog

(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

Crossrefs

Cf. A089633, A188341, A188499, A188529.

Sequence in context: A134313 A307403 A220952 * A181287 A082981 A217787

Adjacent sequences: A188528 A188529 A188530 * A188532 A188533 A188534

Keyword

nonn,base

Author

Vladimir Shevelev, Apr 03 2011

Status

approved