A088028 - OEIS

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A088028

Smallest k such that k^2-1 is a squarefree number with n prime divisors. a(n) = A088027(n)^(1/2).

2, 4, 14, 34, 254, 664, 5116, 18446, 121694, 887314, 7496644, 63124214, 684394346, 3086525014, 25689944554, 453164666954

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

a(4)^2 = 1156 = 34^2 = 3*5*7*11 + 1.

PROG

(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)))))))

CROSSREFS

Cf. A088027.

Sequence in context: A148265 A148266 A000622 * A327459 A336108 A263739

Adjacent sequences: A088025 A088026 A088027 * A088029 A088030 A088031

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 19 2003

EXTENSIONS

More terms from Ray Chandler, Oct 04 2003

Further terms from Thomas Baruchel, Oct 11 2003

STATUS

approved