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Search: id:A155715
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| A155715 |
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Least number expressible as a^2 + k b^2 with positive integers a,b, for each k=1,...,n. |
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+0
4
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| 2, 17, 73, 73, 241, 241, 1009, 1009, 1009, 1009, 7561, 7561, 21961, 32356, 32356, 32356, 44641, 44641, 349924, 349924, 349924, 349924, 1399696, 1399696, 1399696, 3027249, 3027249, 3027249, 4349601, 4349601, 18567396, 18567396, 18567396
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sequence A028372 considers primes with this property, but allowing for nonzero a,b (which obviously is irrelevant for n>2). Up to n=13, the terms of the present sequence are prime without imposing it explicitely and thus coincide with A028372 except for n=2.
a(n) > 10^9 for n >= 47. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 29 2009]
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LINKS
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Donovan Johnson, Table of n, a(n) for n=1..46
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EXAMPLE
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a(1) = 2 = 1^2 + 1^2 is the least number of the sequence A000404 (sum of positive squares). a(2) = 17 = 1^2 + 4^2 = 3^2 + 2*2^2 is the least number in sequence A000404 to be in sequence A154777 (a^2+2b^2)as well. a(3) = 73 = 3^2 + 8^2 = 1^2 + 2*6^2 = 5^2 + 3*4^2 is the least number in the intersection of sequences A000404, A154777 and A092572 (a^2+3b^2).
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PROGRAM
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(PARI) k=1; for( n=1, 10^9, forstep( c=k, 1, -1, for( b=1, sqrtint((n-1)\c), issquare(n-c*b^2) & next(2)); next(2)); print1(n", "); k++; n--)
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CROSSREFS
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Cf. A028372, A000404, A154777, A092572, A097268, A154778, A155707-A155716, A155560-A155578.
Sequence in context: A107815 A042803 A056074 this_sequence A054568 A060352 A002523
Adjacent sequences: A155712 A155713 A155714 this_sequence A155716 A155717 A155718
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), Jan 27 2009
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EXTENSIONS
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a(23)-a(46) and b-file from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 29 2009
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