A366928 a(n) is the smallest nonnegative k such that A301573(k) = n.

1, 0, 6, 12, 20, 41, 42, 56, 72, 90, 110, 155, 156, 182, 270, 271, 272, 306, 379, 380, 420, 462, 551, 552, 600, 650, 702, 756, 812, 870, 930, 1055, 1056, 1122, 1190, 1260, 1405, 1406, 1482, 1560, 1640, 1805, 1806, 1892, 1980, 2254, 2255, 2256, 2352, 2450, 2550, 2652, 2861, 2862, 2970

Offset

0,3

Comments

If negative values were allowed then one could argue a(n) = 1-n from the name of A301573. - David A. Corneth, Nov 13 2023

Links

David A. Corneth, Table of n, a(n) for n = 0..10000

David A. Corneth, PARI program

Formula

a(n) > n^2 for n > 1. - David A. Corneth, Nov 13 2023

Example

a(3) = 12 as 12 is the smallest positive integer that is 3 away from the closest perfect power (namely 9 = 3^2). - David A. Corneth, Nov 12 2023

Prog

(PARI) ispp(n) = {ispower(n) || n==1}; \\ A001597
f(n) = my(k=0); while(!ispp(n+k) && !ispp(n-k), k++); k; \\ A301573
a(n) = my(k=0); while (f(k) != n, k++); k; \\ Michel Marcus, Oct 29 2023
(PARI) \\ See PARI link
(Python)
from itertools import count
from sympy import perfect_power
def A366928(n): return next(m for m in count(0) if next(k for k in count(0) if perfect_power(m+k) or perfect_power(m-k) or m-k==1 or m+k==1) == n) # Chai Wah Wu, Nov 12 2023

Crossrefs

Cf. A001597, A301573.

Sequence in context: A117343 A286290 A240521 * A220211 A028611 A220470

Adjacent sequences: A366925 A366926 A366927 * A366929 A366930 A366931

Keyword

nonn

Author

Dmitry Kamenetsky, Oct 28 2023

Extensions

More terms from Michel Marcus, Oct 29 2023

Status

approved