cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A084675 Product of the first n digits of the Golden Ratio phi = 1.6180339... (treating 0's as if they were 1's).

Original entry on oeis.org

1, 6, 6, 48, 48, 144, 432, 3888, 31104, 248832, 1741824, 6967296, 62705664, 501645312, 4514807808, 18059231232, 144473849856, 577895399424, 4623163195392, 9246326390784, 9246326390784, 36985305563136
Offset: 1

Views

Author

Cino Hilliard, Jun 29 2003

Keywords

Crossrefs

Cf. A074850.

Programs

  • Maple
    Digits:=100: Phi:= (sqrt(5)+1)/2: A084675:=proc(n) options remember: local d: d:=trunc(10*frac(Phi*10^(n-2))): if n=1 then RETURN(d) else RETURN(A084675(n-1)*piecewise(d<>0,d,1)) fi: end; seq(A084675(n),n=1..25); (C. Ronaldo)
  • Mathematica
    FoldList[Times,(RealDigits[GoldenRatio,10,30][[1]]/.(0->1))] (* Harvey P. Dale, Jun 11 2016 *)
  • PARI
    phitorial(n) = { default(realprecision,10000); p = (sqrt(5)+1)/20; default(realprecision,28); for(j=1,n, eitor=1; e1=p; for(x=1,j, d = e1*10; d1=floor(d); if(d1<>0,eitor*=d1); e1 = frac(d); ); print1(eitor",") ) }

Formula

Phi = (sqrt(5)+1)/2 = 1.618033988749894848204586834...

Extensions

Definition clarified by Harvey P. Dale, Jun 11 2016.

A084674 Products of the digits of e excluding 0.

Original entry on oeis.org

2, 14, 14, 112, 224, 1792, 1792, 14336, 28672, 229376, 917504, 4587520, 41287680, 165150720, 825753600, 1651507200, 4954521600, 24772608000, 74317824000, 445906944000, 891813888000, 7134511104000, 49941577728000, 199766310912000, 1398364176384000
Offset: 1

Views

Author

Cino Hilliard, Jun 29 2003

Keywords

Comments

It is interesting that the first 0 occurs in the 14th place of e and the 32nd place in Pi.

Examples

			a(2) = 14 because, e to two places being 2.7, we have 2 * 7 = 14.
a(3) = 14 because e to three places is 2.71.
a(4) = 112 because e to four places is 2.718 and 2 * 7 * 1 * 8 = 112.

Crossrefs

Cf. A074850.

Programs

  • Mathematica
    Rest[FoldList[Times,1,Select[RealDigits[E,10,30][[1]],#!=0&]]] (* Harvey P. Dale, Jan 23 2015 *)
  • PARI
    etorial(n) = { default(realprecision,10000); p = exp(1)/10; default(realprecision,28); for(j=1,n, eitor=1; e1=p; for(x=1,j, d = e1*10; d1=floor(d); if(d1<>0,eitor*=d1); e1 = frac(d); ); print1(eitor",") ) }

Extensions

Corrected and extended by Harvey P. Dale, Jan 23 2015

A084676 Position of the first zero in the decimal expansion of the square root of the n-th prime.

Original entry on oeis.org

14, 5, 5, 11, 10, 3, 6, 13, 26, 9, 13, 2, 3, 12, 9, 4, 15, 4, 24, 19, 5, 19, 4, 11, 9, 1, 1, 1, 1, 1, 23, 18, 4, 40, 4, 7, 9, 13, 14, 16, 6, 9, 5, 16, 3, 4, 9, 12, 3, 11, 18, 14, 14, 27, 3, 11, 4, 6, 12, 6, 7, 34, 48, 9, 7, 4, 7, 11, 9, 16, 12, 50, 9, 7, 18, 5, 6, 34, 1, 1, 1, 1, 1, 1, 1, 3, 8
Offset: 1

Views

Author

Cino Hilliard, Jun 29 2003

Keywords

Examples

			sqrt(1213) = 34.82814953453599722269575212191436263382649518168323557106085786016708, first zero is at position 57.

Crossrefs

Cf. A074850.

Programs

  • PARI
    \ zeros in sqrt(p) where p is prime. frootp(n) = { default(realprecision,100); forprime(x=2,n, r = sqrt(x); \ print(x" "r); v = Vec(Str(r)); c=-1; for(y=1,100, c++; if(v[y] == "0",print1(c","); break) ) ) }
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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