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.

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

Offset: 1

Author

Vladimir Shevelev, Apr 03 2011

Keywords

• nonn
• base

Comments

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

A subsequence of A089633.

Examples

			(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.
		

Links

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

Crossrefs

Cf. A024036, A089633, A188341, A188499.

Programs

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