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Search: id:A090851
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| A090851 |
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Smallest positive k such that phi(2n*k+1) < phi(2n*k), where phi is Euler's totient function. |
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2
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| 157, 131, 41449509748313314446079881572662251904099551759079570289, 103, 87200213, 23228416536806454739917249069243610966391359542839893417, 28651, 59, 16202086544304724831441296633918338274264333181606642583
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note that a(3) = (5 * 7 * 11 * 13 * 17 * 19 * 23 * ... * 149 - 1) / 6. When 2n is the product of distinct small primes, a(n) is very large; e.g. Martin shows that a(15) is a 1116-digit number. The large values of a(n) were computed quickly using a backtracking algorithm.
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REFERENCES
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D. J. Newman, Euler's phi function on arithmetic progressions, Amer. Math. Monthly, Vol. 104, No. 3 (Mar. 1997), pp. 256-257.
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LINKS
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Greg Martin, The smallest solution of phi(30n+1) < phi(30n) is ...
Herman te Riele, On the size of solutions of the inequality phi(ax+b) < phi(ax)
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CROSSREFS
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Cf. A090849 (least k such that phi(1+k*2^n) <= phi(k*2^n)).
Sequence in context: A035824 A006112 A028675 this_sequence A045230 A096704 A140035
Adjacent sequences: A090848 A090849 A090850 this_sequence A090852 A090853 A090854
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Dec 09 2003
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