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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..68.

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

Formula

Numbers n such that A011545(n) is squarefree.

Example

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.

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 *)

Crossrefs

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: A306948 A067241 A360030 * A087792 A192881 A189755

Adjacent sequences: A120940 A120941 A120942 * A120944 A120945 A120946

Keyword

base,nonn

Author

Zak Seidov, Aug 19 2006

Extensions

More terms from Robert G. Wilson v, Aug 21 2006

Status

approved