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

1,2

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

Links

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

Example

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

Prog

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

Crossrefs

Sequence in context: A305855 A018576 A027290 * A367429 A132294 A032330

Adjacent sequences: A131493 A131494 A131495 * A131497 A131498 A131499

Keyword

nonn,base

Author

Randy L. Ekl, Aug 12 2007

Extensions

More terms from Jon E. Schoenfield, Jul 17 2010

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

Status

approved