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A268866 Records in A268865. 3
2, 3, 22, 38, 342, 598, 5462, 9558, 87382, 152918, 1398102, 2446678, 22369622, 39146838 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Conjecture 1) Let m(n) be the position in A268865 corresponding to a(n). Then m(n)=(2/3)*(4^n-1),if n is even, and m(n)=(2/3)*(4^(n-1)-1)+3*4^(n-1), if n is odd.

Conjecture 2) a(n)=2*m(n)+2, if n is even, and a(n)=(7*m+12)/11, if n is odd.

If Conjectures 1,2 are true, then we easily have for even n>=0, m(n) == 0 (mod 10), a(n)== 2 (mod 10), while a(1)= m(1)=3 and for odd n>=3, m(n), a(n) == 8 (mod 10). The sequence {m(n)} begins : 0, 3, 10, 58, 170, 938, 2730, 15018, 43690,...

LINKS

Table of n, a(n) for n=0..13.

Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

CROSSREFS

Cf. A268865.

Sequence in context: A062921 A298470 A083178 * A154254 A264696 A166122

Adjacent sequences:  A268863 A268864 A268865 * A268867 A268868 A268869

KEYWORD

nonn,more

AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Feb 15 2016

STATUS

approved

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Last modified February 22 15:26 EST 2020. Contains 332137 sequences. (Running on oeis4.)