A307463 a(n) is the digit after the appearance of n in the decimal numbers of Pi after all the previous natural numbers of n have already appeared except for 0, and without overlap.

4, 6, 5, 6, 0, 9, 5, 2, 7, 2, 0, 8, 3, 1, 5, 0, 3, 5, 4, 0, 4, 4, 5, 4, 2, 1, 8, 3, 5, 0, 5, 1, 4, 5, 6, 0, 1, 9, 0, 7, 0, 7, 1, 6, 1, 7, 9, 9, 3, 6, 2, 0, 9, 8, 2, 4, 0, 6, 8, 8, 4, 2, 4, 7, 4, 6, 2, 7, 5, 1, 6, 0, 4, 1, 4, 3, 6, 3, 6, 7, 6, 9, 1, 5, 3, 0, 4, 1

Offset

1,1

Comments

All terms appear in the decimal expansion of Pi.

Links

Table of n, a(n) for n=1..88.

Example

See the first decimal digits of Pi for the examples:
3.(1)4159(2)65(3)589793238(4)62643383279(5)0288...
In parentheses the first appearing of natural numbers after all smaller natural numbers have already appeared.
- FIRST ELEMENT a(1):
For n=1, the first '1' appears in the first decimal place of Pi, and the next decimal digit is '4', so a(1)=4.
- DIGIT POSITION:
For n=4, although the first 4 appears in the 2 decimal place, not all the previous natural numbers of 4 have appeared, so, after 1, 2, and 3 have appeared (in this order), then, a(4) will be the next digit after the next 4. So a(4)=6.
- N WITH MORE THAN 1 DIGIT:
In the decimal digits of Pi: ...50284(10)270193852(11)05...
For n with more than 1 digit, a(n) is, after all the previous natural numbers have appeared, the next digit after all the digits of n have appeared consecutively. Example: a(10)=2, a(11)=0.
- NO OVERLAP:
In the decimal digits of Pi: ...52230825(33)44685035...730359825(34)904...
Example: for n=33, a(33)=4, but, as there is no overlap, the '3' cannot be used again with the '4' for n=34, so a(34) is defined by the next 34: a(34)=9.

Prog

(PARI) lista(nn, t=10^5) = {default(realprecision, t); my(d, k=1, v=digits(floor(Pi*10^t))); for(n=1, nn, d=digits(n); while(v[k..k+#d-1]!=d, k++); k+=#d; print1(v[k], ", ")); } \\ Jinyuan Wang, Feb 18 2021

Crossrefs

Cf. A000796, A103186.

Sequence in context: A271365 A088559 A092526 * A243396 A140243 A366872

Adjacent sequences: A307460 A307461 A307462 * A307464 A307465 A307466

Keyword

nonn,base

Author

Marc Bofill Janer, Apr 09 2019

Extensions

More terms from Jinyuan Wang, Feb 18 2021

Status

approved