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Search: id:A089578
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| A089578 |
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Decimal expansion of the Mersenne prime 2^20996011 - 1. |
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+0
1
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| 1, 2, 5, 9, 7, 6, 8, 9, 5, 4, 5, 0, 3, 3, 0, 1, 0, 5, 0, 2, 0, 4, 9, 4, 3, 0, 9, 5, 7, 4, 8, 2, 4, 3, 1, 1, 4, 5, 5, 9, 9, 3, 4, 1, 6, 0, 8, 5, 3, 5, 1, 8, 3, 5, 9, 5, 2, 2, 5, 4, 6, 7, 0, 1, 2, 5, 6, 5, 4, 9, 8, 7, 6, 8, 9, 0, 8, 3, 5, 1, 5, 6, 0, 2, 2, 1, 2, 4, 0, 0, 9, 6, 8, 0, 2, 8, 2, 8, 5, 3, 6, 1, 3, 2, 5
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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We can compute the digits of 2^p directly by noting that
...p....p*log(2)/log(10)....plog10(2)..
..2.=.10................=.10...........
This result is 10^(i+f) where i is the integer part and f the fractional part. Then 10^f will produce a decimal number i.d1d2d3d4.... where i is an integer from 1 to 9 (zero cannot occur in i) and d1,d2..are the digits in the fractional part where 0 is allowed. So i is the first digit in 2^p,d1 the second,d2 the third etc. The expansion is self evident in the PARI program. This routine allows the direct computation of the digits of any base to a power: k^p = 10^plog10(k).
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PROGRAM
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(PARI) \ digits of the 40th Mersenne prime: 2^20996011 - 1 p = 20996011 digitsm40(n, p) = { default(realprecision, n); p10 = frac(p*log(2)/log(10)); v = 10^p10; for(j=1, n, d=floor(v); v=frac(v)*10; print1(d", ") ) }
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CROSSREFS
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Sequence in context: A065225 A018878 A021389 this_sequence A020852 A053477 A104956
Adjacent sequences: A089575 A089576 A089577 this_sequence A089579 A089580 A089581
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KEYWORD
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easy,cons,nonn,fini
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 29 2003
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