A059903 Periodic part of continued fraction for sqrt(n), encoded by raising successive primes to the terms. If sqrt(n)=c0+[c1,c2,c3...] then a(n)=2^c1*3^c2*5^c3*...

1, 4, 18, 1, 16, 324, 72030, 162, 1, 64, 5832, 2916, 372027810, 10588410, 1458, 1, 256, 104976, 1036385881030500, 26244, 9421689827550, 4946387159463750, 1556496270, 13122, 1, 1024, 1889568, 2542277241000, 76256028326940, 236196

Offset

1,2

Comments

Could be made less gigantic by omitting final terms in continued fraction, which are always 2*c0.

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = A059900(A059904(n)).

Example

sqrt(14) = 3+[1,2,1,6] so a(14) = 2^1*3^2*5^1*7^6 = 10588410.

Crossrefs

Cf. A059904, A059900, A003285.

Sequence in context: A154131 A132554 A077275 * A227540 A353701 A246133

Adjacent sequences: A059900 A059901 A059902 * A059904 A059905 A059906

Keyword

easy,nonn

Author

Marc LeBrun, Feb 07 2001

Extensions

Offset corrected by Sean A. Irvine, Oct 14 2022

Status

approved