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Search: id:A114844
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| A114844 |
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Sum of first n digits of pi to digit-wise power of first n digits of e. |
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1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Pi Digits.
Eric Weisstein's World of Mathematics, e.
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FORMULA
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a(n) = SUM[i = 1 to n] A000796(i)^A001113(i).
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000796, A001113, A039661, A059850, A114605.
Sequence in context: A061445 A088710 A020199 this_sequence A005381 A099616 A140209
Adjacent sequences: A114841 A114842 A114843 this_sequence A114845 A114846 A114847
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2006
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