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A240924 Digital root of squares of numbers not divisible by 2, 3 or 5. 2
1, 4, 4, 7, 1, 1, 7, 4, 7, 1, 7, 4, 4, 7, 1, 7, 4, 7, 1, 1, 7, 4, 4, 1, 1, 4, 4, 7, 1, 1, 7, 4, 7, 1, 7, 4, 4, 7, 1, 7, 4, 7, 1, 1, 7, 4, 4, 1, 1, 4, 4, 7, 1, 1, 7, 4, 7, 1, 7, 4, 4, 7, 1, 7, 4, 7, 1, 1, 7, 4, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This period 24 repeating sequence is palindromic.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1,-1,2,-2,1,1,-2,1,1,-2,1).

FORMULA

From Colin Barker, Sep 21 2019: (Start)

G.f.: x*(1 + x)^2*(1 - 4*x^2 + 12*x^3 - 27*x^4 + 45*x^5 - 53*x^6 + 45*x^7 - 27*x^8 + 12*x^9 - 4*x^10 + x^12) / ((1 - x)*(1 - x + x^2)*(1 - x^2 + x^4)*(1 - x^4 + x^8)).

a(n) = 2*a(n-1) - a(n-2) - a(n-3) + 2*a(n-4) - a(n-5) - a(n-6) + 2*a(n-7) - 2*a(n-8) + a(n-9) + a(n-10) - 2*a(n-11) + a(n-12) + a(n-13) - 2*a(n-14) + a(n-15) for n>15.

(End)

EXAMPLE

The first 8 numbers not divisible by 2, 3 or 5 are 1,7,11,13,17,19,23,29; with squares 1,49,121,169,289,361,529,841 and digital root sequence of 1,4,4,7,1,1,7,4.

PROG

(Python)

A240924 = [1 + (n*n-1) % 9 for n in range(1, 10**3, 2) if n % 3 and n % 5 ]

# Chai Wah Wu, Sep 03 2014

(PARI) Vec(x*(1 + x)^2*(1 - 4*x^2 + 12*x^3 - 27*x^4 + 45*x^5 - 53*x^6 + 45*x^7 - 27*x^8 + 12*x^9 - 4*x^10 + x^12) / ((1 - x)*(1 - x + x^2)*(1 - x^2 + x^4)*(1 - x^4 + x^8)) + O(x^100)) \\ Colin Barker, Sep 21 2019

CROSSREFS

Cf. A007775, A166923.

Sequence in context: A090531 A198138 A300709 * A319034 A282468 A196463

Adjacent sequences:  A240921 A240922 A240923 * A240925 A240926 A240927

KEYWORD

nonn,base,easy

AUTHOR

Gary Croft, Aug 15 2014

STATUS

approved

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)