OFFSET
1,1
COMMENTS
There is a triangular array of n dots, having at least three rows, having row sizes 1, 1+2x, 1+4x, 1+6x, ... iff n is in this sequence (where x equals all the natural numbers). - Peter Woodward, Apr 24 2015
The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 1, 32, 381, 3929, 39703, 398182, 3985220, 39863899, 398676976, 3986887465, ... . Apparently, the asymptotic density of this sequence exists and equals 0.3986... . - Amiram Eldar, Jun 06 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
E.g., consider k = 91: we can take d = 7, 7 divides 91 and 6 divides 90, so 91 is in the sequence.
MAPLE
N:= 1000: # to get all terms <= N
{seq(seq(d+k*d*(d-1), k=1..floor((N-d)/d/(d-1))), d=3..floor(sqrt(N)))};
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Apr 24 2015
MATHEMATICA
fQ[n_] := Block[{d = Select[ Take[ Divisors@ n, {2, -2}], # > 2 &]}, Union[IntegerQ /@ ((n - 1)/(d - 1))][[ -1]]]; Select[ Range@ 175, !PrimeQ@ # && fQ@ # &] (* Robert G. Wilson v, May 04 2008 *)
PROG
(PARI) is(k) = fordiv(k, d, if(d > 2 && d < k && !((k-1) % (d-1)), return(1))); 0; \\ Amiram Eldar, Jun 06 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
J. Perry (johnandruth(AT)jrperry.orangehome.co.uk), Apr 13 2008
EXTENSIONS
Definition, terms and offset corrected by M. F. Hasler, May 01 2008
Edited by N. J. A. Sloane, May 10 2008
STATUS
approved