A049522 -id:A049522 - cp's OEIS frontend

A084145 First digit occurring consecutively at least n times in Pi's decimal expansion.

3, 3, 1, 9, 9, 9, 3, 4, 7, 6, 1, 7, 8, 9, 6, 6, 6

Offset: 1

Rick L. Shepherd, May 23 2003

A simple variation on this sequence could ignore the 3 before the decimal point, making a(1)=1 instead.

			a(4)=a(5)=a(6) = 9 because there are (exactly) six consecutive 9's occurring with starting index A049522(4)=A049522(5)=A049522(6) = 763 and there are no runs of 4, 5, 6, or more consecutive equal digits having a smaller starting index.
The first occurrence of a run of at least seven consecutive equal digits occurs at starting index A049522(7) = 710101. The run consists of exactly seven 3's so a(7) = 3 [=A084144(7)] and also A049523(7) = 710101.

Dave Andersen, Pi-Search Page
Timothy Mullican, 50 trillion digits of pi
Peter Trüb, 22.4 trillion digits of pi
Eric Weisstein's World of Mathematics, Pi Digits

Cf. A049522 (starting index), A084144 (consecutively exactly n times), A049523 (starting index for A084144 runs).

a(10)-a(14) added by Dmitry Petukhov, Jan 13 2020

a(15)-a(17) from Dmitry Petukhov, Oct 30 2021

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

Felix Fröhlich, Oct 19 2016

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

Cf. A001620, A049522, A244601, A244602, A277259, A277260, A277533.

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

Felix Fröhlich, Oct 19 2016

Cf. A001620, A049522, A244601, A244602, A277259, A277260, A277532.

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)

a(n) = A001620(A277532(n)) * A002275(n).

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A084145 First digit occurring consecutively at least n times in Pi's decimal expansion.

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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.

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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.

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