A242973 Positions in both e and Pi where both digits in the same position are prime.

1, 5, 9, 16, 17, 18, 25, 29, 30, 34, 40, 54, 64, 65, 74, 77, 84, 90, 92, 94, 100, 103, 112, 115, 124, 132, 136, 137, 138, 143, 144, 159, 178, 179, 180, 195, 204, 211, 217, 236, 242, 253, 275, 283, 286, 293, 302, 303, 305, 307, 317, 321, 326, 334, 339, 344, 347

Offset: 1

Author

Philip Mizzi, May 28 2014

Keywords

• base
• nonn

Examples

			Pi = 3.1415926535897932384626...
.....|....|...|......|||........
_e = 2.7182818284590452353602...
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052055, A073302, A153031.

Programs

Mathematica

Module[{digs=350,p,e,th},p=RealDigits[Pi,10,digs][[1]];e=RealDigits[E,10,digs][[1]];th = Thread[{p,e}];Position[If[AllTrue[#,PrimeQ],1,0]&/@th,1]]//Flatten (* Harvey P. Dale, Jan 28 2023 *)

PARI

\p 1000
e=Vec(Str(exp(1)/10)); p=Vec(Str(Pi/10)); for(n=1, #e-9, if(isprime(eval(e[n+2])) && isprime(eval(p[n+2])), print1(n", "))) \\ Jens Kruse Andersen, Jul 23 2014

Extensions

Definition clarified by Harvey P. Dale, Jan 28 2023