A186771 Numbers m such that A186711(m) = 1.

1, 2, 3, 6, 12, 27, 48, 130, 252, 705, 1386, 2295, 7125, 17316, 31959, 51054, 74601, 102600, 351315, 748440, 2123189, 4198848, 6975417, 10452896, 14631285, 19510584, 25090793, 31371912, 38353941, 46036880, 54420729, 63505488, 73291157, 83777736, 94965225, 106853624, 119442933, 132733152

Offset

1,2

Comments

Greatest common divisor of A003586(a(n)) and A003586(a(n)+1) is 1.

Links

Table of n, a(n) for n=1..38.

Formula

A186927(n) = A003586(a(n)); A186928(n) = A003586(a(n) + 1).

Example

n = 12, a(12) = 2295:
A003586(2295) = 19342813113834066795298816 = 2^84,
A003586(2296) = 19383245667680019896796723 = 3^53 and GCD(2^84,3^53) = 1.

Mathematica

seq[lim_] := Module[{s = {}, pow3, c2, c3a, c3b}, Do[c2 = c[2^i]; pow3 = 3^Floor[i*Log[3, 2]]; c3a = c[pow3]; c3b = c[3*pow3]; If[c3a + 1 == c2, AppendTo[s, c3a]]; If[c2 + 1 == c3b, AppendTo[s, c2]], {i, 0, c[lim]}]; s]; c[n_] := Sum[1 + Floor[Log[3, n/2^i]], {i, 0, Log2[n]}]; seq[10^14] (* Amiram Eldar, Apr 16 2025 *)

Prog

(Haskell)
import Data.List (findIndices)
a186771 n = a186771_list !! (n-1)
a186771_list = map (+ 1) $ findIndices (== 1) a186711_list
(PARI) c(n) = sum(i=0, logint(n, 2), 1 + logint(n\2^i, 3));
list(lim) = {my(pow3, c2, c3a, c3b); for(i = 0, c(lim), c2 = c(2^i); pow3 = 3^logint(2^i, 3); c3a = c(pow3); c3b = c(3*pow3); if(c3a + 1 == c2, print1(c3a, ", ")); if(c2 + 1 == c3b, print1(c2, ", "))); } \\ Amiram Eldar, Apr 16 2025

Crossrefs

Cf. A003586, A186711, A186927, A186928.

Sequence in context: A373182 A339150 A024422 * A019525 A108915 A082395

Adjacent sequences: A186768 A186769 A186770 * A186772 A186773 A186774

Keyword

nonn

Author

Reinhard Zumkeller, Feb 26 2011

Extensions

a(22)-a(33) from Donovan Johnson, Mar 04 2011

a(34)-a(38) from Amiram Eldar, Apr 16 2025

Status

approved