A131496 Values of n such that n^Pi starts with the digits n.

1, 3, 9, 74, 15940, 136888, 401150, 29585255, 86699685, 2181946705, 6394201903, 18738229439, 54912442215, 160921090214, 4049856052188, 34779553385863, 875287288851249, 7516835314214410, 64553448748440886, 189174091165714089, 1624598582798015801, 4760891422045743495, 119816022336026653554

Offset: 1

Author

Randy L. Ekl, Aug 12 2007

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Max Alekseyev, Table of n, a(n) for n = 1..300

Programs

PARI

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

Extensions

More terms from Jon E. Schoenfield, Jul 17 2010

Terms a(21) onward from Max Alekseyev, Sep 08 2013