The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A307582 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A307582

Position of the first occurrence of (0, 1, ..., n-1) in the digits of Pi written in base n.
(history; published version)

#12 by Alois P. Heinz at Tue Apr 07 19:48:49 EDT 2020

STATUS

proposed

approved

#11 by Chai Wah Wu at Tue Apr 07 19:10:01 EDT 2020

STATUS

editing

proposed

#10 by Chai Wah Wu at Tue Apr 07 19:09:48 EDT 2020

DATA

2, 7, 188, 2264, 27931, 110808, 23489363, 97438020

EXTENSIONS

a(7)-a(9) from Chai Wah Wu, Apr 07 2020

STATUS

approved

editing

#9 by Susanna Cuyler at Tue Apr 16 15:30:17 EDT 2019

STATUS

proposed

approved

#8 by M. F. Hasler at Mon Apr 15 20:40:21 EDT 2019

STATUS

editing

proposed

#7 by M. F. Hasler at Mon Apr 15 20:40:13 EDT 2019

FORMULA

A307581(n) <= a(n) <= A307583(n).

CROSSREFS

Cf. A307582 A307581 (first occurrence of any permutation of 0 .. n-1, in base-n digits of Pi).

Cf. A307583 (start of last permutation of {0 .. n-1} not to occur earlier, in base-n digits of Pi).

#6 by M. F. Hasler at Mon Apr 15 19:33:07 EDT 2019

DATA

2, 7, 188, 2264, 27931

PROG

(PARI) A307582(n, x=Pi, m=Mod(sum(i=1, n-1, i*n^(n-1-i)), n^n))={for(k=0, 999, oo, x\n^-k==m&&return(k-n+1)) \\ Ensure sufficient precision of the argument x = pi.

STATUS

proposed

editing

#5 by M. F. Hasler at Mon Apr 15 19:29:32 EDT 2019

STATUS

editing

proposed

#4 by M. F. Hasler at Mon Apr 15 19:28:52 EDT 2019

EXAMPLE

Pi written in base 2 is 11.001...[2], so the first "01" occurs at position a(2) = 2.

Pi written in base 3 is 10.010211012...[3], we see that the first occurrence of the string "012" is at position a(3) = 7.

Pi written in base 4 is 3.02100333...[4]; the string of digits "0123" does not occur until position a(4) = 188.

PROG

(PARI) A307582(n, x=Pi, m=Mod(sum(i=1, n-1, i*n^(n-1-i)), n^n))={for(k=0, 999, x\n^-k==m&&return(k-n+1)) \\ Ensure sufficient precision of the argument x = pi.

CROSSREFS

Cf. A307582 (first occurrence of any permutation of 0 .. n-1).

Cf. A068987 (occurrence of 123...n in decimal digits of Pi), A121280.

Discussion

Mon Apr 15

19:29

M. F. Hasler: I put kw "base" although the sequence as a whole does not depend on an (arbitrary) choice of base.

#3 by M. F. Hasler at Mon Apr 15 19:22:06 EDT 2019

NAME

allocated for M. F. Hasler

Position of the first occurrence of (0, 1, ..., n-1) in the digits of Pi written in base n.

DATA

2, 7, 188

OFFSET

2,1

COMMENTS

Position refers to the digit where there required sequence (0, ..., n-1) starts. Position = k means the digit '0' occurs as digit corresponding to the weight n-^k (and thereafter, the digit '1' will correspond to n^-(k+1) etc): e.g., the first digit after the decimal point has position 1.

KEYWORD

allocated

nonn,base,more

AUTHOR

M. F. Hasler, Apr 15 2019

STATUS

approved

editing