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A120943 Numbers n such that merging first n digits in decimal expansion of Pi (A000796) gives a squarefree composite number. 2
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; refs; listen; history; text; internal format)
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: A022769 A306948 A067241 * 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

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Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)