login
A355711
Starts of runs of 3 consecutive numbers with the same number of 5-smooth divisors.
3
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 15 2022
STATUS
approved