A323637 -id:A323637 - cp's OEIS frontend

A323638 Nested square root sqrt(b(n) - sqrt(b(n-1) - ... - sqrt(b(1))...)), where b(n) = A323637(n).

1, 1, 2, 1, 3, 1, 4, 2, 2, 3, 2, 4, 3, 3, 4, 4, 5, 2, 5, 3, 5, 4, 6, 3, 6, 4, 7, 3, 7, 4, 8, 4, 9, 4, 10, 4, 11, 5, 5, 6, 5, 7, 5, 8, 5, 9, 5, 10, 5, 11, 6, 6, 7, 6, 8, 6, 9, 6, 10, 6, 11, 7, 7, 8, 7, 9, 7, 10, 7, 11, 8, 8

Offset: 1

Ivan Neretin, Jan 21 2019

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

Cf. A323637.

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.

Original entry on oeis.org

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

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

A permutation of positive integers.

Ivan Neretin, Table of n, a(n) for n = 1..10000
Mathematics Stack Exchange, a_n is the smallest positive integer number such that ...

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

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

cp's OEIS Frontend

A323638 Nested square root sqrt(b(n) - sqrt(b(n-1) - ... - sqrt(b(1))...)), where b(n) = A323637(n).

Views

Author

Keywords

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI