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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.
5
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
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
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Apr 03 2011
STATUS
approved