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Search: id:A075821
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| A075821 |
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List of possible last two digits (leading zeros omitted) of perfect powers. |
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+0
4
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| 0, 1, 3, 4, 7, 8, 9, 11, 12, 13, 16, 17, 19, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 56, 57, 59, 61, 63, 64, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 83, 84, 87, 88, 89, 91, 92, 93, 96, 97, 99
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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An equivalent definition: Numbers equal to the final two digits of their 21st, 41st, 61st, etc. powers. - Henry Bottomley (se16(AT)btinternet.com), Nov 25 2004
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FORMULA
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Consists of all numbers below 100 except those which are a multiple of 2 but not 4 and those which are a multiple of 5 but not 25. - Henry Bottomley (se16(AT)btinternet.com), Nov 25 2004
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EXAMPLE
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With leading zeros, the initial terms are 00, 01, 03, 04, 07, 08, 09. Corresponding smallest perfect powers are 100, 2401, 658503, 2304, 16807, 140608, 2209.
1 (01!) is OK because the perfect power 2401=49^2 ends with 01. 9 (09!) is OK because the perfect power 2209=47^2 ends with 09.
11 is in the sequence since 11^21=7400249944258160101211 and the final two digits are 11.
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CROSSREFS
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Cf. A010809, A100990.
Sequence in context: A092754 A061094 A100991 this_sequence A120515 A047545 A105941
Adjacent sequences: A075818 A075819 A075820 this_sequence A075822 A075823 A075824
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KEYWORD
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full,fini,nonn,base
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Oct 14 2002
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 06 2007
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