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A031435
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Reversal point for powers of consecutive natural numbers.
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1
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1, 2, 4, 7, 9, 12, 15, 18, 21, 25, 28, 32, 35, 39, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 83, 87, 91, 95, 100, 104, 109, 113, 118, 122, 127, 131, 136, 141, 145, 150, 155, 159, 164, 169, 174, 179, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248
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OFFSET
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1,2
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COMMENTS
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a(n+1) is smallest k such that floor((1+1/n)^k) == 0 mod(n). A065560(n) is not a strictly increasing sequence, but a(n) is a strictly increasing sequence. - Benoit Cloitre, May 23 2002
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LINKS
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Table of n, a(n) for n=1..60.
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FORMULA
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If bases are N, N+1, the reversal point is floor( log(1+N)/log(1+1/N) ).
For n>1, ceiling((n+1/2)*log(n)) is an approximation to a(n) which is valid for all n <= 1000 except n=77 and n=214. - Benoit Cloitre, May 23 2002; corrected by Franklin T. Adams-Watters, Dec 16 2005
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EXAMPLE
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2 from: 3^2 >2^3 but 3^1<2^2; 4 from: 4^4>3^5 but 4^3<3^4; 7 from; 5^7>4^8 but 5^6<4^7; 9 from: 6^9>5^10 but 6^8<5^9; 12 from: 7^12>6^13 but 7^11<6^12; etc.
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PROG
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(PARI) for(n=1, 100, print1(ceil((n+1/2)*log(n)), ", ")) (Valid for 1<n<77)
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CROSSREFS
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Cf. A065560.
Sequence in context: A184735 A184583 A189379 * A065560 A134886 A024193
Adjacent sequences: A031432 A031433 A031434 * A031436 A031437 A031438
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KEYWORD
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nonn
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AUTHOR
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Donald Mintz (djmintz(AT)home.com)
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EXTENSIONS
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More terms from Benoit Cloitre, May 23 2002
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STATUS
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approved
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