A120943 - OEIS

%I #12 Jul 08 2023 18:41:49

%S 3,5,8,10,11,12,13,14,15,16,18,19,21,22,23,25,27,28,30,31,32,34,39,40,

%T 41,43,44,45,46,48,50,51,53,54,57,58,59,60,62,63,65,66,67,69,73,76,77,

%U 80,81,82,83,84,87,88,90,92,93,94,96,97,98,99,100,102,103,104,109,111

%N Numbers n such that merging first n digits in decimal expansion of Pi (A000796) gives a squarefree composite number.

%C 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.

%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Java Applet: Factorization using the Elliptic Curve Method.</a>

%H H. Mishima, <a href="https://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/de_pi000.htm">Factorizations of many number sequences</a>

%H H. Mishima, <a href="https://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/de_pi100.htm">Factorizations of many number sequences</a>

%F Numbers n such that A011545(n) is squarefree.

%e n=3: first 3 digits give 314=2*157

%e n=5: first 5 digits give 31415=5*61*103

%e n=8: 31415926=2*1901*8263

%e n=10: 3141592653=3*107*9786893

%e n=11: 31415926535=5*7*31*28954771

%e n=12: 314159265358=2*157079632679, etc.

%t (* 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_ *)

%t 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 *)

%Y Cf. A000796 = Decimal expansion of Pi, A011545 = Decimal expansion of pi truncated to n places.

%Y Cf. A000796, A011545.

%Y Complement of A120943 is A121865.

%K base,nonn

%O 1,1

%A _Zak Seidov_, Aug 19 2006

%E More terms from _Robert G. Wilson v_, Aug 21 2006