The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A225401 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A225401

10-adic integer x such that x^3 = -7/9.
(history; published version)

#22 by Alois P. Heinz at Thu Apr 14 10:51:56 EDT 2022

STATUS

editing

approved

#21 by Alois P. Heinz at Thu Apr 14 10:51:38 EDT 2022

MAPLE

b:= proc(n) option remember; `if`(n<2, 3*n,

irem(b(n-1)+3*(9*b(n-1)^3+7), 10^n))

end:

a:= n-> (b(n+1)-b(n))/10^n:

seq(a(n), n=0..100); # Alois P. Heinz, Apr 14 2022

STATUS

approved

editing

#20 by Susanna Cuyler at Tue Aug 13 08:12:22 EDT 2019

STATUS

reviewed

approved

#19 by Joerg Arndt at Tue Aug 13 07:13:43 EDT 2019

STATUS

proposed

reviewed

#18 by Seiichi Manyama at Tue Aug 13 07:12:15 EDT 2019

STATUS

editing

proposed

#17 by Seiichi Manyama at Tue Aug 13 00:43:08 EDT 2019

PROG

b = (a + 3 * (9 * a ** 3 - + 7)) % (10 ** (i + 2))

#16 by Seiichi Manyama at Tue Aug 13 00:42:33 EDT 2019

FORMULA

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, 3, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 7) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - Seiichi Manyama, Aug 13 2019

PROG

(Ruby)

def A225401(n)

ary = [3]

a = 3

n.times{|i|

b = (a + 3 * (9 * a ** 3 - 7)) % (10 ** (i + 2))

ary << (b - a) / (10 ** (i + 1))

a = b

}

ary

end

p A225401(100) # Seiichi Manyama, Aug 13 2019

#15 by Seiichi Manyama at Tue Aug 13 00:40:30 EDT 2019

FORMULA

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 7) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - Seiichi Manyama, Aug 13 2019

CROSSREFS

Cf. A225410, A309600.

STATUS

approved

editing

#14 by Joerg Arndt at Thu Aug 08 10:07:14 EDT 2019

STATUS

proposed

approved

#13 by Seiichi Manyama at Thu Aug 08 10:06:16 EDT 2019

STATUS

editing

proposed