A073161 - OEIS

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A073161

Nested floor product of n and fractions (p_k + 1)/p_k where p_k is k-th prime.

1, 4, 6, 10, 12, 20, 21, 26, 28, 36, 38, 46, 50, 56, 57, 64, 69, 80, 81, 87, 92, 99, 104, 112, 116, 122, 126, 133, 140, 146, 147, 155, 169, 172, 176, 185, 188, 198, 202, 210, 213, 222, 228, 237, 242, 253, 254, 264, 270, 279, 280, 289, 298, 303, 305, 318, 323

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Sequence consists only of composite numbers.

LINKS

Table of n, a(n) for n=1..57.

FORMULA

a(n) = [...[[[n*(1+1/2)]*(1+1/3)]*(1+1/5)]...*(1+1/p_k)]..., where [x] = floor of x and p_k is the k-th prime; this infinite nested floor product will eventually level-off at a(n). Alternatively, for n>=1, let b(0, n)=n and b(k, n) = floor( b(k-1, n)*(1 + 1/p_k) ), for k=1..m, then a(n)=b(m, n) where m is smallest integer such that p_m > a(n).

EXAMPLE

a(4) = 10 since [[[[4*(1+1/2)]*(1+1/3)]*(1+1/5)]*(1+1/7)] = [[[6*(1+1/3)]*(1+1/5)]*(1+1/7)] = [[8*(1+1/5)]*(1+1/7)] = [9*(1+1/7)] = 10.

CROSSREFS

Sequence in context: A122171 A310580 A353966 * A272777 A310581 A310582

Adjacent sequences: A073158 A073159 A073160 * A073162 A073163 A073164

KEYWORD

easy,nonn,changed

AUTHOR

Paul D. Hanna, Jul 29 2002

STATUS

approved

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