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A071901
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n-th decimal digit of the fractional part of the square root of the n-th prime.
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5
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4, 3, 6, 7, 2, 1, 6, 4, 3, 1, 3, 8, 8, 0, 4, 2, 7, 4, 9, 3, 1, 4, 2, 0, 4, 1, 8, 6, 4, 9, 8, 8, 1, 4, 3, 4, 0, 8, 4, 1, 0, 2, 8, 6, 3, 2, 3, 7, 4, 7, 6, 6, 2, 5, 0, 1, 2, 3, 1, 3, 7, 4, 4, 7, 7, 4, 3, 6, 9, 6, 1, 2, 1, 9, 8, 9, 4, 2, 9, 9, 3, 5, 6, 9, 0, 4, 9, 3, 8, 6, 9, 6, 3, 6, 4, 2, 6, 3, 5, 9, 3, 7, 8, 9, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Regarded as a decimal fraction, 0.4367216431388... is likely to be an irrational number.
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REFERENCES
| Bryan Birch, Mathematical Fallacies and Paradoxes, Dover 1982; suggested by pages 120,121 and 122
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FORMULA
| a(n)=Floor[10^n*Sqrt(Prime(n))]-10*Floor[10^(n-1)*Sqrt(Prime(n))]
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EXAMPLE
| Sqrt(2)=1.4142135... -> the first decimal digit is 4, sqrt(3)=1.7320508... -> the 2nd decimal digit is 3, sqrt(5)=2.2360679... -> the 3rd decimal digit is 6, etc.
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MAPLE
| A071901 := proc(n) local p; p := ithprime(n) ; Digits := p+3 ; floor(10^n*sqrt(p)) mod 10 ; end proc: seq(A071901(n), n=1..120) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 17 2009]
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MATHEMATICA
| q[n_] := Mod[ Floor[10^n*Sqrt[ Prime[n]]], 10]; Table[ q[n], {n, 1, 105}]
Table[rd=RealDigits[N[Sqrt[Prime[n]], 2*n]]; rd[[1, rd[[2]]+n]], {n, 10000, 100000, 10000}] (from Zak Seidov, Nov 17 2009)
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PROG
| Contribution from Michael Porter (michael_b_porter(AT)yahoo.com), Dec 11 2009: (Start)
(PARI) A071901(n) = {local(r, x, d); r=sqrtint(prime(n)); x=100*(prime(n)-r^2);
for(digits=1, n, d=0; while((20*r+d)*d <= x, d++);
d--; /* while loop overshoots correct digit */
x=100*(x-(20*r+d)*d); r=10*r+d); d} (End)
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CROSSREFS
| Sequence in context: A131603 A062302 A021233 * A103476 A021700 A197829
Adjacent sequences: A071898 A071899 A071900 * A071902 A071903 A071904
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KEYWORD
| nonn,base,nice
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 12 2002
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com) and Henry Bottomley (se16(AT)btinternet.com), Jun 13 2002
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