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Values of n such that n^Pi starts with the digits n.
2

%I #15 Feb 27 2017 02:52:41

%S 1,3,9,74,15940,136888,401150,29585255,86699685,2181946705,6394201903,

%T 18738229439,54912442215,160921090214,4049856052188,34779553385863,

%U 875287288851249,7516835314214410,64553448748440886,189174091165714089,1624598582798015801,4760891422045743495,119816022336026653554

%N Values of n such that n^Pi starts with the digits n.

%C Values can occur only at ceiling(x^k) where k is a nonnegative integer and x = 10^(1/(Pi-1)) = 2.9305032470520496858554269... (i.e., the solution of x^Pi = 10*x). - _Jon E. Schoenfield_, Jul 17 2010

%H Max Alekseyev, <a href="/A131496/b131496.txt">Table of n, a(n) for n = 1..300</a>

%e 74 is a term of this sequence because 74^Pi = 745357.5218745..., which starts with 74.

%o (PARI) s=1;for(i=1,500000,s=i^Pi; while(s-i>11,s=s/10); if(floor(s)==i,printp1(i,", "),))

%K nonn,base

%O 1,2

%A _Randy L. Ekl_, Aug 12 2007

%E More terms from _Jon E. Schoenfield_, Jul 17 2010

%E Terms a(21) onward from _Max Alekseyev_, Sep 08 2013