A120943 Numbers n such that merging first n digits in decimal expansion of Pi (A000796) gives a squarefree composite number.
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
Offset: 1
Examples
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.
Links
- 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
Crossrefs
Programs
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Mathematica
(* 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 *) Module[{nn=120,p,c},p=RealDigits[Pi,10,nn][[1]];Select[Range[nn], CompositeQ[ c=FromDigits[Take[p,#]]]&&SquareFreeQ[c]&]] (* Harvey P. Dale, Mar 25 2015 *)
Formula
Numbers n such that A011545(n) is squarefree.
Extensions
More terms from Robert G. Wilson v, Aug 21 2006
Comments