A114844 Sum of first n digits of Pi to digit-wise power of first n digits of e.

9, 10, 14, 15, 40, 43046761, 43046763, 44726379, 44726404, 44732965, 44733590, 44766358, 432186847, 432186848, 432193409, 432193652, 432193656, 432193683, 432226451, 432226515, 432273171, 432273172, 432273208, 432338744, 432340931

Offset

1,1

Comments

The 331st digit of Pi and the 331st digit of e are both 0, so to generate any additional terms of the sequence beyond 330 terms one would have to define 0^0 to be either 0 or 1. - Harvey P. Dale, Aug 05 2014

Links

Harvey P. Dale, Table of n, a(n) for n = 1..300

Eric Weisstein's World of Mathematics, Pi Digits.

Eric Weisstein's World of Mathematics, e.

Formula

a(n) = Sum_{i=1..n} A000796(i)^A001113(i).

Example

Since Pi =
3.1415926535897932384626433832795028841971693993751058209749445923078164062...
and e =
2.71828182845904523536028747135266249775724709369995957496696762772407663...
we have:
a(1) = 9 = 3^2.
a(2) = 10 = 3^2 + 1^7.
a(3) = 14 = 3^2 + 1^7 + 4^1.
a(4) = 15 = 3^2 + 1^7 + 4^1 + 1^8.
a(5) = 40 = 3^2 + 1^7 + 4^1 + 1^8 + 5^2.
a(6) = 43046761 = 3^2 + 1^7 + 4^1 + 1^8 + 5^2 + 9^8.

Mathematica

With[{nn=30}, Accumulate[RealDigits[Pi, 10, nn][[1]]^RealDigits[E, 10, nn] [[1]]]] (* Harvey P. Dale, Aug 05 2014 *)

Crossrefs

Cf. A000796, A001113, A039661, A059850, A114605.

Sequence in context: A088710 A020199 A227943 * A194593 A005381 A175090

Adjacent sequences: A114841 A114842 A114843 * A114845 A114846 A114847

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Feb 19 2006

Status

approved