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Search: id:A114605
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| A114605 |
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Sum of first n digits of e to digit-wise power of first n digits of pi. |
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+0
2
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| 8, 15, 16, 24, 56, 134217784, 134217785, 134479929, 134479961, 134480473, 134481497, 134872122, 522292611, 522292611, 522554755, 522554880, 522554884, 522554911, 522945536, 522945617
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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e^(pi i) = -1. Decimal expansion of e^pi = A039661. Here we are taking digit-by-digit e^pi and summing the partial terms. a(10) = 134480473 = 2^3 + 7^1 + 1^4 + 8^1 + 2^5 + 8^9 + 1^2 + 8^6 + 2^5 + 8^3 is the first prime in this sequence. a(20) = 522945617 is the second prime in this sequence. This sum of digit-wise exponentiation of decimal expansions of real constants is binary transformation of integer sequences, as are the individual terms without summation.
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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] A001113(i)^A000796(i).
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EXAMPLE
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Since e = 2.71828182845904523536028747135266249775724709369995957496696762772407663...
and pi =
3.1415926535897932384626433832795028841971693993751058209749445923078164062...
a(1) = 8 = 2^3.
a(2) = 15 = 2^3 + 7^1.
a(3) = 16 = 2^3 + 7^1 + 1^4.
a(4) = 24 = 2^3 + 7^1 + 1^4 + 8^1.
a(5) = 56 = 2^3 + 7^1 + 1^4 + 8^1 + 2^5.
a(6) = 134217784 = 2^3 + 7^1 + 1^4 + 8^1 + 2^5 + 8^9.
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CROSSREFS
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Cf. A000796, A001113, A039661.
Sequence in context: A103706 A134990 A126852 this_sequence A031103 A133157 A014544
Adjacent sequences: A114602 A114603 A114604 this_sequence A114606 A114607 A114608
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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 17 2006
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