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A114844 Sum of first n digits of pi to digit-wise power of first n digits of e. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This demonstrates the noncommutativity of the binary transformation of integer sequences, "sum of digit-wise exponentiation of decimal expansions of real constants," by comparison with A114605 "sum of first n digits of e to digit-wise power of first n digits of pi." Assuming equidistribution of the digits of e and pi, there should be an infinite number of k such that a(k) = A114605(k). The first primes in this sequence are a(13) = 432186847, a(19) = 432226451.

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 to 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

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Last modified September 28 21:45 EDT 2020. Contains 337414 sequences. (Running on oeis4.)