A338319 a(n) is the smallest positive integer m such that n appears as the denominator of a semiconvergent to sqrt(m).

1, 2, 2, 3, 2, 8, 2, 7, 5, 11, 3, 2, 5, 7, 3, 11, 2, 13, 10, 6, 5, 11, 8, 23, 10, 3, 14, 12, 2, 31, 7, 32, 13, 23, 8, 20, 10, 5, 15, 40, 2, 22, 10, 23, 39, 27, 15, 7, 6, 51, 26, 41, 19, 71, 5, 3, 17, 14, 24, 11, 26, 41, 15, 8, 17, 54, 21, 72, 6, 2, 13, 5, 17, 96

Offset

1,2

Comments

a(n) <= A338307(n).

Links

Table of n, a(n) for n=1..74.

Prog

(PARI) { A338319(n) = my(a, b, r, q, v); if(n==1, return(1)); for(m=1, oo, if(issquare(m), next); r=sqrtint(m); a=0; b=1; q=[1, 0]~; while(q[2]<n, v=(r+a)\b; a=b*v-a; b=(m-a^2)/b; q=[0, 1; 1, v]*q; ); if(Mod(q[2], q[1])==n, return(m)); ); }

Crossrefs

Cf. A338307, A338320.

Sequence in context: A015999 A225244 A345281 * A369748 A280583 A177047

Adjacent sequences: A338316 A338317 A338318 * A338320 A338321 A338322

Keyword

nonn

Author

Max Alekseyev, Oct 22 2020

Status

approved