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

Author

Zhining Yang, Mar 11 2025

Keywords

• nonn
• base
• easy

Comments

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

Examples

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

Links

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

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).

Programs

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}]