A242973 - OEIS

%I #15 Jan 28 2023 19:38:17

%S 1,5,9,16,17,18,25,29,30,34,40,54,64,65,74,77,84,90,92,94,100,103,112,

%T 115,124,132,136,137,138,143,144,159,178,179,180,195,204,211,217,236,

%U 242,253,275,283,286,293,302,303,305,307,317,321,326,334,339,344,347

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

%H Jens Kruse Andersen, <a href="/A242973/b242973.txt">Table of n, a(n) for n = 1..10000</a>

%e Pi = 3.1415926535897932384626...

%e .....|....|...|......|||........

%e _e = 2.7182818284590452353602...

%t 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 *)

%o (PARI) \p 1000

%o 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

%Y Cf. A052055, A073302, A153031.

%K base,nonn

%O 1,2

%A _Philip Mizzi_, May 28 2014

%E Definition clarified by _Harvey P. Dale_, Jan 28 2023