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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)