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Search: id:A166051
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| A166051 |
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Non-square integers of the form 4n+1 for which Sum_{i=1..u} J(i,4n+1) is never negative for any u in range [1,(2n)], where J(i,k) is the Jacobi symbol. |
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2
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OFFSET
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1,1
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COMMENT
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Conjecture: There are no more terms after 165. (Checked up to A016813(290511) = 1162045.) If this is true, then also 5, 13 and 37 are only 4k+1 primes in A080114.
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PROGRAM
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(MIT Scheme with macro MATCHING-POS by AK):
(define (A166051 n) (A016813 (index_for_a166051 n)))
(define index_for_a166051 (MATCHING-POS 1 0 (lambda (n) (let ((w (A016813c n)) (hp (A005843 n))) (let loop ((i 1) (s 1)) (cond ((< s 0) #f) ((>= i hp) (zero? s)) (else (loop (1+ i) (+ s (jacobi-symbol (1+ i) w))))))))))
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CROSSREFS
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Setwise difference of A016754 and A166049.
Sequence in context: A166090 A065766 A034170 this_sequence A160170 A060004 A076408
Adjacent sequences: A166048 A166049 A166050 this_sequence A166052 A166053 A166054
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 08 2009
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