A323635 Lexicographically earliest sequence of distinct positive integers such that the nested square root sqrt(a(n) + sqrt(a(n-1) + ... + sqrt(a(1))...)) is an integer.

1, 3, 2, 7, 6, 13, 5, 22, 4, 33, 10, 12, 21, 11, 32, 19, 20, 31, 30, 43, 9, 45, 18, 44, 29, 58, 8, 60, 17, 59, 28, 75, 16, 76, 27, 94, 15, 95, 26, 115, 14, 116, 25, 138, 24, 163, 23, 190, 35, 42, 57, 41, 74, 40, 93, 39, 114, 38, 137, 37, 162, 36, 189, 50, 56, 73, 55, 92, 54, 113, 53, 136

Offset

1,2

Comments

A permutation of positive integers.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Mathematics Stack Exchange, a_n is the smallest positive integer number such that ...

Prog

(PARI) lista(nn) = {my(va = vector(nn), lastsq); va[1] = 1; lastsq = 1; for (n=2, nn, my(k = ceil(sqrt(sqrtint(lastsq)))); while (#select(x->(x==(k^2-sqrtint(lastsq))), va), k++); va[n] = k^2-sqrtint(lastsq); lastsq = k^2; ); va; } \\ Michel Marcus, Oct 13 2020

Crossrefs

Cf. A323636 (values of the square roots), A323637 (similar definition with minus).

Sequence in context: A122355 A175433 A058646 * A125718 A268821 A014841

Adjacent sequences: A323632 A323633 A323634 * A323636 A323637 A323638

Keyword

nonn,look

Author

Ivan Neretin, Jan 21 2019, following a suggestion from Edward Turkevich

Status

approved