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; rowland's prime-generating function (define (A106108 limit) ; initial sequence (let loop ((n 1) (as '(7))) (if (<= limit n) (reverse as) (let* ((n (+ n 1)) (a (+ (car as) (gcd n (car as))))) (loop n (cons a as)))))) (define (A132199 limit) ; differences (let loop ((n 2) (prev 7) (ds '())) (if (< limit (- n 1)) (reverse ds) (let* ((next (+ prev (gcd n prev))) (d (- next prev))) (loop (+ n 1) next (cons d ds)))))) (define (A137613 limit) ; only primes (let loop ((n 2) (prev 7) (ps '())) (if (<= limit (length ps)) (reverse ps) (let* ((next (+ prev (gcd n prev))) (d (- next prev))) (loop (+ n 1) next (if (= d 1) ps (cons d ps))))))) (define (least-prime-divisor n) (do ((d 3 (+ d 2))) ((zero? (modulo n d)) d))) (define (shortcut limit) (let loop ((limit limit) (k 5) (as '(5))) (if (= limit 1) (reverse as) (let* ((k (+ k (car as) -1)) (a (least-prime-divisor k))) (loop (- limit 1) k (cons a as)))))) (display (A106108 65)) (newline) (display (A132199 104)) (newline) (display (A137613 72)) (newline) (display (shortcut 72)) (newline)
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