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 1-5 of 5 results.

A244601 Position of first occurrence of n consecutive equal digits in the decimal expansion of e starting after the decimal point.

Original entry on oeis.org

1, 31, 47, 723, 4992, 89296, 210482, 384340, 110702779, 419970418
Offset: 1

Views

Author

Felix Fröhlich, Jul 01 2014

Keywords

Comments

Position 31 is occupied by the first of two consecutive 6's. Position 47 is occupied by the first of three consecutive 9's. Position 723 is occupied by the first of four consecutive 8's.

Examples

			Decimal expansion of e:
2.|7|18281828459045235360287471352|66|24977572470936|999|59574966967627724..
		

Crossrefs

Cf. A001113. Resulting repdigits are A244602.

Programs

  • Mathematica
    e = Rest[First[RealDigits[E, 10, 2000000]]];
    A244601 = ConstantArray[0, 8];
    For[i = 1, i <= Length[e], i++,
      t = e[[i]]; c = 1;
      While[e[[i + c]] == t, c++];
      If[A244601[[c]] == 0, A244601[[c]] = i;  i = i + c - 1; Continue[]]
    ]; A244601 (* Robert Price, Sep 07 2019 *)

Extensions

a(5)-(8) from Jens Kruse Andersen, Jul 20 2014
a(9)-(10) from Felix Fröhlich, Aug 26 2014
Prepended a(1), Felix Fröhlich, Aug 31 2014

A277259 Position of initial digit of first string of n consecutive equal digits in the decimal expansion of the Golden ratio (phi), starting after the decimal point.

Original entry on oeis.org

1, 5, 129, 1216, 6399, 99788, 771950, 771950, 314529194
Offset: 1

Views

Author

Felix Fröhlich, Oct 07 2016

Keywords

Examples

			1205th to 1230th digits of phi are as follows: ...63972321340444494873023154...
The 1216th digit is occupied by the first of four consecutive 4's and there is no earlier occurrence of four or more consecutive equal digits, so a(4) = 1216.
		

Crossrefs

A277260 Value of decimal number corresponding to the string of equal digits starting at position A277259(n) after the decimal point in the decimal expansion of the Golden ratio (phi).

Original entry on oeis.org

6, 33, 222, 4444, 99999, 555555, 5555555, 55555555, 333333333
Offset: 1

Views

Author

Felix Fröhlich, Oct 07 2016

Keywords

Examples

			1205th to 1230th digits of phi are as follows: ...63972321340444494873023154...
The 1216th digit is occupied by the first of four consecutive 4's and there is no earlier occurrence of four or more consecutive equal digits, so a(4) = 4444.
		

Crossrefs

Formula

a(n) = A001622(A277259(n)+1) * A002275(n).

A277532 Position of first occurrence of at least n consecutive equal digits in the decimal expansion of the Euler-Mascheroni constant, starting after the decimal point.

Original entry on oeis.org

0, 1, 72, 2346, 3422, 3892
Offset: 1

Views

Author

Felix Fröhlich, Oct 19 2016

Keywords

Comments

Smallest k such that A001620(k) = A001620(k+m) for all m with 0 <= m < n.

Crossrefs

Programs

  • PARI
    emstring(n) = default(realprecision, n+10); my(x=Euler); floor(x*10^n)
    emdigit(n) = emstring(n)-10*emstring(n-1)
    searchstrpos(n) = my(x=1, i=1); while(1, my(y=x+1); while(emdigit(y)==emdigit(x), y++; i++); if(i >= n, return(x-1)); i=1; x++)
    a(n) = searchstrpos(n)

A277533 Value of decimal number corresponding to the string of equal digits starting at position A277532(n) after the decimal point in the decimal expansion of the Euler-Mascheroni constant.

Original entry on oeis.org

5, 77, 777, 0, 0, 333333
Offset: 1

Views

Author

Felix Fröhlich, Oct 19 2016

Keywords

Crossrefs

Programs

  • PARI
    emstring(n) = default(realprecision, n+10); my(x=Euler); floor(x*10^n)
    emdigit(n) = emstring(n)-10*emstring(n-1)
    searchstrval(n) = my(x=1, i=1); while(1, my(y=x+1); while(emdigit(y)==emdigit(x), y++; i++); if(i >= n, return(emdigit(x)*(10^n-1)/9)); i=1; x++)
    a(n) = searchstrval(n)

Formula

a(n) = A001620(A277532(n)) * A002275(n).
Showing 1-5 of 5 results.