A044075 Numbers k such that the string 3,2 occurs in the base-4 representation of k but not of k-1.

14, 30, 46, 56, 62, 78, 94, 110, 120, 126, 142, 158, 174, 184, 190, 206, 222, 224, 248, 254, 270, 286, 302, 312, 318, 334, 350, 366, 376, 382, 398, 414, 430, 440, 446, 462, 478, 480, 504, 510, 526, 542, 558, 568, 574, 590, 606

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Numbers whose base-4 representation ends in 3,2 followed by some number of zeros and includes no other 3,2. - Franklin T. Adams-Watters, Dec 04 2006

Not the same as A055039 - see A124169.

A 4-automatic set: membership is determined by comparing the base-4 representation of the number to the regular expression /[012]*(3+([01][012]*)?)*320*/. - Charles R Greathouse IV, Feb 11 2012 [corrected by Pontus von Brömssen, Jan 12 2019]

Alternatively, numbers whose base-4 representation is in the language generated by the regular expression /([012]|3*[01])*3+20*/. - Pontus von Brömssen, Jan 17 2019

Links

• R. J. Mathar, Table of n, a(n) for n = 1..10000
• Index entries for 2-automatic sequences.

Programs

Maple

has32 := proc(n) local shft : shft := n : while shft > 0 do if shft mod 16 = 14 then RETURN(true) ; fi : shft := floor(shft/4) : od : RETURN(false) ; end: isA044075 := proc(n) if has32(n) and not has32(n-1) then return(true): else return(false) : fi : end: n := 1 : a := 1 : while n <= 10000 do while not isA044075(a) do a := a+1 : od : printf("%d %d ",n,a) : a := a+1 : n := n+1 : od : # R. J. Mathar, Dec 07 2006

Mathematica

Flatten[Position[Partition[Table[If[MemberQ[Partition[IntegerDigits[n, 4], 2, 1], {3, 2}], 1, 0], {n, 1000}], 2, 1], {0, 1}]] + 1 (* Vincenzo Librandi, Aug 19 2015 *)