cp's OEIS Frontend

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

%I A114844 #25 Feb 16 2025 08:33:00
%S A114844 9,10,14,15,40,43046761,43046763,44726379,44726404,44732965,44733590,
%T A114844 44766358,432186847,432186848,432193409,432193652,432193656,432193683,
%U A114844 432226451,432226515,432273171,432273172,432273208,432338744,432340931
%N A114844 Sum of first n digits of Pi to digit-wise power of first n digits of e.
%C A114844 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
%H A114844 Harvey P. Dale, <a href="/A114844/b114844.txt">Table of n, a(n) for n = 1..300</a>
%H A114844 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PiDigits.html">Pi Digits</a>.
%H A114844 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/e.html">e</a>.
%F A114844 a(n) = Sum_{i=1..n} A000796(i)^A001113(i).
%e A114844 Since Pi =
%e A114844 3.1415926535897932384626433832795028841971693993751058209749445923078164062...
%e A114844 and e =
%e A114844 2.71828182845904523536028747135266249775724709369995957496696762772407663...
%e A114844 we have:
%e A114844 a(1) = 9 = 3^2.
%e A114844 a(2) = 10 = 3^2 + 1^7.
%e A114844 a(3) = 14 = 3^2 + 1^7 + 4^1.
%e A114844 a(4) = 15 = 3^2 + 1^7 + 4^1 + 1^8.
%e A114844 a(5) = 40 = 3^2 + 1^7 + 4^1 + 1^8 + 5^2.
%e A114844 a(6) = 43046761 = 3^2 + 1^7 + 4^1 + 1^8 + 5^2 + 9^8.
%t A114844 With[{nn=30},Accumulate[RealDigits[Pi,10,nn][[1]]^RealDigits[E,10,nn] [[1]]]] (* _Harvey P. Dale_, Aug 05 2014 *)
%Y A114844 Cf. A000796, A001113, A039661, A059850, A114605.
%K A114844 base,easy,nonn
%O A114844 1,1
%A A114844 _Jonathan Vos Post_, Feb 19 2006