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A188529 Numbers which contain only the digit 3 in their base-4 representation, with at most one exception. If the exception is the most-significant digit, it must be the digit 1 or 2, otherwise the exception must be the digit 2. 6
1, 2, 3, 7, 11, 14, 15, 31, 47, 59, 62, 63, 127, 191, 239, 251, 254, 255, 511, 767, 959, 1007, 1019, 1022, 1023, 2047, 3071, 3839, 4031, 4079, 4091, 4094, 4095, 8191, 12287, 15359, 16127, 16319, 16367, 16379, 16382, 16383, 32767, 49151, 61439, 64511, 65279, 65471, 65519 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence lists the positive binomial coefficient predictors in base 4. For definition, see paper in link.

A subsequence of A089633.

LINKS

Table of n, a(n) for n=1..49.

V. Shevelev, Binomial Coefficient Predictors, Journal of Integer Sequences, Vol. 14 (2011), Article 11.2.8

EXAMPLE

(767)_10 = (23333)_4 contains only digits 3, with the exception the leading digit which is 2. Therefore 767 is in the sequence.

(4091)_10 = (333323)_4 contains only digits 3, with the exception a digit 2.

MAPLE

isA188529 := proc(n) local dgs , n3, p, d; dgs := convert(n, base, 4); n3 := 0 ; for p from 1 to nops(dgs) do d := op(p, dgs) ; if d <> 3 then n3 := n3+1 ; if n3 >=2 then return false; end if; if p < nops(dgs) and d <> 2 then return false; end if; if p = nops(dgs) and d = 0 then return false; end if; end if; end do: return true; end proc:

A188529 := proc(n) option remember; local a; if n = 1 then 1; else for a from procname(n-1)+1 do if isA188529(a) then return a; end if; end do; end if; end proc:

seq(A188529(n), n=1..50) ; # R. J. Mathar, Apr 03 2011

CROSSREFS

Cf. A024036, A089633, A188341, A188499.

Sequence in context: A113244 A040152 A323353 * A174060 A285278 A092353

Adjacent sequences:  A188526 A188527 A188528 * A188530 A188531 A188532

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.)