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A060458
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Consider the final n decimal digits of 2^j for all values of j. They are periodic. Sequence gives maximal value seen in these n digits.
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2
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8, 96, 992, 9984, 99968, 999936, 9999872, 99999744, 999999488, 9999998976, 99999997952, 999999995904, 9999999991808, 99999999983616, 999999999967232, 9999999999934464, 99999999999868928, 999999999999737856
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Index entries for sequences related to final digits of numbers
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FORMULA
| a(n)=10^n-2^n=2^n*(5^n-1)
a(n)=12*a(n-1)-20*a(n-2) O.g.f.:1/(1-10x)-1/(1-2x)
-Geoffrey Critzer, Dec 15 2011.
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EXAMPLE
| Maximum of the last 4 digits of powers of 2 is 9984=10000-16. It occurs at 2^254. 2^254=289480223.....01978282409984 (with 77 digits,last 4 ones are ...9984); The period length of the last-4-digit segment is A005054(4)=500. For n=4 period:amplitude=9984,phase=254.
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MATHEMATICA
| RecurrenceTable[{a[n] == 12 a[n - 1] - 20 a[n - 2], a[0] == 0, a[1] == 8}, a[n], {n, 1, 20}] (*Geoffrey Critzer, Dec 15 2011*)
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PROG
| (Other) sage: [10^n - 2^n for n in xrange(1, 19)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
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CROSSREFS
| Cf. A000079, A005054, A060460.
Cf. A016134 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
Sequence in context: A069650 A066424 A099675 * A173834 A098430 A034177
Adjacent sequences: A060455 A060456 A060457 * A060459 A060460 A060461
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KEYWORD
| base,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Apr 09 2001
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