The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A152575 A triangle of coefficients of polynomials with roots as the Pi-digits base ten A000796(n)=d(n):d(1)=3; p(x,n)=-d(1)*Product[x-d(m),{m,2,n}]. 0
 -3, 3, -3, -12, 15, -3, 12, -27, 18, -3, -60, 147, -117, 33, -3, 540, -1383, 1200, -414, 60, -3, -1080, 3306, -3783, 2028, -534, 66, -3, 6480, -20916, 26004, -15951, 5232, -930, 84, -3, -32400, 111060, -150936, 105759, -42111, 9882, -1350, 99, -3, 97200 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS p(x,n)=Product[(x-i)^a(i),{i,0,9}]: a(i) is the count number of the way the digits occur by the n-th digit. The limiting polynomial is: pL(x)=Product[(x-i),{i,0,9}]= -362880 x + 1026576 x^2 - 1172700 x^3 + 723680 x^4 - 269325 x^5 + 63273 x^6 - 9450 x^7 + 870 x^8 - 45 x^9 + x^10; since if the digits occur equally: p(x,Infinity)=-3*Product[(x-i),{i,0,9}]^(Infinity/10). Or at the n-th digits equality: p(x,n)=-3*Product[(x-i),{i,0,9}]^(n/10). The n+1 digit: p(x,n+1)=p(x,n)*(x-d(n+1)). LINKS FORMULA Pi-digits base ten A000796(n)=d(n): p(x,n)=-d(1)*Product[x-d(m),{m,2,n}]. EXAMPLE {-3}, {3, -3}, {-12,15, -3}, {12, -27, 18, -3}, {-60, 147, -117, 33, -3}, {540, -1383, 1200, -414, 60, -3}, {-1080, 3306, -3783, 2028, -534, 66, -3}, {6480, -20916, 26004, -15951, 5232, -930, 84, -3}, {-32400, 111060, -150936, 105759, -42111, 9882, -1350, 99, -3}, {97200, -365580, 563868, -468213, 232092, -71757, 13932, -1647, 108, -3} MATHEMATICA Clear[a, p, n, m]; a = Delete[Flatten[RealDigits[Pi, 10, 100]], 100]; p[x_, n_] := If[n == 1, -a[[1]], -a[[1]]*Product[x - a[[m]], {m, 2, n}]]; Table[CoefficientList[p[x, n], x], {n, 1, 10}] Flatten[%] CROSSREFS Sequence in context: A156715 A133797 A225073 * A170851 A052900 A024947 Adjacent sequences:  A152572 A152573 A152574 * A152576 A152577 A152578 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Dec 08 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 29 08:46 EDT 2021. Contains 346340 sequences. (Running on oeis4.)