A340643 Numbers k such that the two perfect powers immediately adjacent to k^2 both have exponents greater than 2.

2, 3, 5, 15, 26, 46, 82, 89, 90, 129, 323, 362, 401, 420, 610, 624, 840, 2024, 2703, 2808, 6888, 12099, 15963, 19320, 24650, 29930, 33490, 36482, 39203, 45795, 47523, 52440, 66050, 69168, 83408, 94248, 94863, 103683, 114284, 164399, 185364, 206442, 222785, 227530, 229180

Offset

1,1

Comments

Within the range of the data, a(n)^2 = A340642(n), i.e., no 3 immediately consecutive perfect powers x^p1, y^p2, z^p3 with min (p1, p2, p3) > 2 are seen. Is there a counterexample?

Links

David A. Corneth, Table of n, a(n) for n = 1..611 (first 181 terms from Hugo Pfoertner)

Prog

(PARI) a340643(limit)={my(p2=999, p1=2, n2=1, n1=4); for(n=5, limit, my(p0=ispower(n)); if(p0>1, if(issquare(n1)&p2>2&p0>2, print1(sqrtint(n1), ", ")); n2=n1; n1=n; p2=p1; p1=p0))};
a340643(10^8)
(PARI) upto(n) = {n *= n; my(v = List(), res = List([2])); for(i = 2, sqrtnint(n, 3), for(e = 3, logint(n, i), listput(v, i^e) ); ); listsort(v, 1); for(i = 1, #v - 1, if(sqrtint(v[i]) + 1 == sqrtint(v[i+1]) - issquare(v[i+1]), listput(res, sqrtint(v[i+1]-issquare(v[i+1]))); ) ); res }

Crossrefs

Cf. A000290, A001597, A025479, A076467, A097054, A111245, A153158, A340642, A340700, A340701.

Sequence in context: A296051 A248613 A024781 * A120755 A227633 A270011

Adjacent sequences: A340640 A340641 A340642 * A340644 A340645 A340646

Keyword

nonn

Author

Hugo Pfoertner, Jan 14 2021

Extensions

More terms from David A. Corneth, Jan 14 2021

Status

approved