A153130 - OEIS

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A153130

Period 6: repeat 1,2,4,8,7,5.

1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`Digital root of 2^n.` `A regular version of Pitoun's sequence: a(n)=A029898(n+1).` `Also obtained from permutations of A141425, A020806, A070366, A153110, A153990, A154127, A154687, or A154815.` `This sequence and its (again period 6) repeated differences produce the table` `..1,..2,..4,..8,..7,..5,..1,..2,..4,..8,..7,...` `..1,..2,..4,.-1,.-2,.-4,..1,..2,..4,.-1,.-2,...` `..1,..2,.-5,.-1,.-2,..5,..1,..2,.-5,.-1,.-2,...` `..1,.-7,..4,.-1,..7,.-4,..1,.-7,..4,.-1,..7,...` `.-8,.11,.-5,..8,-11,..5,.-8,.11,.-5,..8,-11,...` `.19,-16,.13,-19,.16,-13,.19,-16,.13,-19,.16,...` `-35,.29,-32,.35,-29,.32,-35,.29,-32,.35,-29,...` `.64,-61,.67,-64,.61,-67,.64,-61,.67,-64,.61,...` `If each entry of this table is read modulo 9 we obtain the very regular table` `..1,..2,..4,..8,..7,..5,..1,..2,..4,..8,..7,...` `..1,..2,..4,..8,..7,..5,..1,..2,..4,..8,..7,...` `..1,..2,..4,..8,..7,..5,..1,..2,..4,..8,..7,...` `..1,..2,..4,..8,..7,..5,..1,..2,..4,..8,..7,...` `..1,..2,..4,..8,..7,..5,..1,..2,..4,..8,..7,...` `..1,..2,..4,..8,..7,..5,..1,..2,..4,..8,..7,...` `Also the decimal expansion of the constant 125/1001. [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2009]` `Terms of the simple continued fraction of 254/(sqrt(548587)-565). [From Paolo P. Lava (paoloplava(AT)gmail.com), Feb 17 2009]`
	LINKS	`Index to sequences with linear recurrences with constant coefficients, signature (1,0,-1,1).`
	FORMULA	`a(n)=(1/30){29(n mod 6)+19[(n+1) mod 6]+14[(n+2) mod 6]-11[(n+3) mod 6]-[(n+4) mod 6]+4[(n+5) mod 6], with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Dec 19 2008]` `a(n)+a(n+3) = 9 = A010734(n).` `G.f.: (1+x+2x^2+5x^3)/((1-x)(1+x)(1-x+x^2)). [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2009]` `a(n) = A082365(n) mod 9. [Paul Curtz (bpcrtz(AT)free.fr), Mar 31 2009]`
	MATHEMATICA	`Flatten[Table[{1, 2, 4, 8, 7, 5}, {20}]]`
	CROSSREFS	`Cf. A030132, A145389, A189510.` `Sequence in context: A071571 A201568 A029898 * A021406 A065075 A001370` `Adjacent sequences: A153127 A153128 A153129 * A153131 A153132 A153133`
	KEYWORD	`nonn,easy`
	AUTHOR	`Paul Curtz (bpcrtz(AT)free.fr), Dec 19 2008`
	EXTENSIONS	`Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2009`

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Last modified February 16 15:54 EST 2012. Contains 205932 sequences.