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Search: id:A088028
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| A088028 |
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Smallest k such that k^2-1 is a squarefree number with n prime divisors. a(n) = A088027(n)^(1/2). |
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2
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| 2, 4, 14, 34, 254, 664, 5116, 18446, 121694, 887314, 7496644, 63124214, 684394346, 3086525014, 25689944554, 453164666954
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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a(4)^2 = 1156 = 34^2 = 3*5*7*11 + 1.
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PROGRAM
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(Scheme program from Thomas Baruchel); (define primes '(2 3 5 7 ... 999983)) (compute n) returns A088028(n) (or #f if prime list is too short) computation takes a reasonable amount of time for n <= 16 (slower than "brutal" method for small values of n, but soon becomes much quicker). Result is certified to be the smallest.
(define (compute* n mmax prod offset) (do ((i offset (+ i 1)) (l (length primes))) ((>= (* prod (do ((j 0 (+ j 1)) (p 1)) ((= j n) p) (set! p (* p (list-ref primes (+ i j)))))) mmax) mmax) (let ((p (* prod (list-ref primes i)))) (if (> n 1) (set! mmax (compute* (- n 1) mmax p (+ i 1))) (let ((s (inexact->exact (floor (sqrt (+ p 1)))))) (if (= (* s s) (+ p 1)) (set! mmax p)))))))
(define (compute n) (let* ((p (reverse (cdr primes))) (mmax (apply * (cons (car p) (list-tail p (- (length p) (- n 1)))))) (r (compute* n mmax 1 1))) (if (= mmax r) #f (inexact->exact (floor (sqrt (+ r 1)))))))
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CROSSREFS
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Cf. A088027.
Sequence in context: A148265 A148266 A000622 this_sequence A135960 A006611 A007462
Adjacent sequences: A088025 A088026 A088027 this_sequence A088029 A088030 A088031
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 19 2003
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 04 2003
Further terms from Thomas Baruchel (baruchel(AT)users.sourceforge.net), Oct 11 2003
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