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Search: id:A120943
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| A120943 |
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Numbers n such that merging first n digits in decimal expansion of Pi (A000796) gives a square-free composite number. |
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+0
2
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| 3, 5, 8, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 22, 23, 25, 27, 28, 30, 31, 32, 34, 39, 40, 41, 43, 44, 45, 46, 48, 50, 51, 53, 54, 57, 58, 59, 60, 62, 63, 65, 66, 67, 69, 73, 76, 77, 80, 81, 82, 83, 84, 87, 88, 90, 92, 93, 94, 96, 97, 98, 99, 100, 102, 103, 104, 109, 111
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note that the indices here differ by one from those in WIFC (World Integer Factorization Center), N = int(pi*10^(n)), by Hisanori Mishima. Therefore to H. Mishima's index add one.
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LINKS
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Dario Alejandro Alpern, Java Applet: Factorization using the Elliptic Curve Method.
H. Mishima, Factorizations of many number sequences
H. Mishima, Factorizations of many number sequences
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FORMULA
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Numbers n such that A011545(n) is square-free
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EXAMPLE
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n=3: first 3 digits give 314=2*157
n=5: first 5 digits give 31415=5*61*103
n=8: 31415926=2*1901*8263
n=10: 3141592653=3*107*9786893
n=11: 31415926535=5*7*31*28954771
n=12: 314159265358=2*157079632679, etc.
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MATHEMATICA
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(* first do *) Needs["NumberTheory`NumberTheoryFunctions`"] (* then *) p = RealDigits[Pi, 10, 100][[1]]; fQ[n_] := Block[{fd = FromDigits@ Take[p, n]}, !PrimeQ@fd && SquareFreeQ@fd]; Select[Range@81, fQ@# &] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000796 = Decimal expansion of Pi, A011545 = Decimal expansion of pi truncated to n places.
Cf. A000796, A011545.
Complement of A120943 is A121865.
Sequence in context: A032682 A022769 A067241 this_sequence A087792 A141436 A073608
Adjacent sequences: A120940 A120941 A120942 this_sequence A120944 A120945 A120946
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KEYWORD
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base,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Aug 19 2006
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EXTENSIONS
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More terms from Robert G. Wilson v, Aug 21 2006
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