A381980 a(n) is the first position where the digits of n occur simultaneously in the decimal expansions of Pi and e.

331, 95, 17, 18, 263, 326, 21, 40, 206, 13, 13422, 428, 500, 6426, 12896, 11172, 17951, 962, 9710, 2857, 9261, 4782, 21688, 17, 26172, 2526, 2060, 2900, 5375, 6167, 10097, 13009, 9287, 12651, 4175, 840, 38691, 11997, 14119, 3519, 4684, 21785, 7662, 1798, 1253, 10869, 9157, 7216, 3430, 13191, 5148, 1843, 10790

Offset

0,1

Comments

The digits of the decimal expansions are numbered starting with 1 at the initial digits 3 (resp. 2).

Links

Zhining Yang, Table of n, a(n) for n = 0..9999

Example

a(9) = 13 because the first "9" appears simultaneously in Pi and e at index 13:
Pi = 3.1415926535897932384626...
     . ...........|.............
 e = 2.7182818284590452353602...

Mathematica

pi=RealDigits[Pi, 10, 40000][[1]];
e=RealDigits[E, 10, 40000][[1]];
Table[Intersection[SequencePosition[pi, IntegerDigits[k]][[All, 1]], SequencePosition[e, IntegerDigits[k]][[All, 1]]][[1]], {k, 0, 52}]

Crossrefs

Cf. A000796 (Pi), A001113 (e).

Cf. A032445 (positions in Pi), A088576 (positions in e).

Cf. A052055 (positions in both Pi and e indicate a common digit).

Sequence in context: A104476 A140908 A256586 * A319718 A319921 A365596

Adjacent sequences: A381977 A381978 A381979 * A381981 A381982 A381983

Keyword

nonn,base,easy

Author

Zhining Yang, Mar 11 2025

Status

approved