A355711 Starts of runs of 3 consecutive numbers with the same number of 5-smooth divisors.

33, 85, 93, 145, 213, 265, 393, 445, 453, 475, 505, 633, 685, 753, 805, 813, 865, 933, 985, 993, 1045, 1113, 1165, 1293, 1345, 1353, 1405, 1430, 1533, 1585, 1624, 1653, 1705, 1713, 1765, 1833, 1885, 1893, 1945, 2013, 2065, 2193, 2245, 2253, 2275, 2305, 2433, 2485

Offset

1,1

Comments

Numbers k such that A355583(k) = A355583(k+1) = A355583(k+2).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

33 is a term since A355583(33) = A355583(34) = A355583(35) = 2.

Mathematica

f[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); s = {}; m = 3; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 2500}]; s

Prog

(PARI) s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
s1 = s(1); s2 = s(2); for(k = 3, 2500, s3 = s(k); if(s1 == s2 && s2 == s3, print1(k-2, ", ")); s1 = s2; s2 = s3);

Crossrefs

Cf. A355583.

Subsequence of A355710.

A355712 is a subsequence.

Similar sequences: A005238, A006073, A045939, A332313, A332387.

Sequence in context: A075039 A359746 A039833 * A250732 A080700 A292366

Adjacent sequences: A355708 A355709 A355710 * A355712 A355713 A355714

Keyword

nonn

Author

Amiram Eldar, Jul 15 2022

Status

approved