

A152247


a(1) = 1, a(2) = 3; thereafter a(n) is the smallest odd positive integer not yet occurring in the sequence such that gcd(a(n), a(n1)) > 1.


3



1, 3, 9, 15, 5, 25, 35, 7, 21, 27, 33, 11, 55, 45, 39, 13, 65, 75, 51, 17, 85, 95, 19, 57, 63, 49, 77, 91, 105, 69, 23, 115, 125, 135, 81, 87, 29, 145, 155, 31, 93, 99, 111, 37, 185, 165, 117, 123, 41, 205, 175, 119, 133, 147, 129, 43, 215, 195, 141, 47, 235, 225, 153
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OFFSET

1,2


COMMENTS

From Matthew Vandermast, Nov 21 2009: (Start)
Odd analog of the EKG sequence. Cf. A064413.
In contrast to A064413, there are at least 2 different patterns by which primes > a(2) are introduced into the sequence. 5 is the first of many primes p that are immediately preceded in the sequence by 3p and immediately followed by 5p. For p = 7, 19, or 31, p is immediately preceded by 5p and immediately followed by 3p. (End)
In fact, based on the first 10000 terms, it appears that apart from the three exceptions 7, 19, and 31, primes p are always preceded by 3*p and followed by 5*p. The graph is very similar to the graph of the EKG sequence.  N. J. A. Sloane, Oct 29 2020


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000


MAPLE

M:= 10000;
N:= 100000;
V:= Array(0..100000, 0): # V = hit?
A[1]:= 1: # A = sequence
A[2]:= 3: V[3]:= 1:
for n from 3 to M do # get candidates S for next term
sw:=1;
S:= {seq(seq(k*p, k=1..N/p), p=numtheory:factorset(A[n1]))};
for s in sort(convert(S, list)) do
if type(s, odd) and V[s] = 0 then
A[n]:= s; V[s]:=1; sw := 1; break; fi;
od;
if sw=1 then lprint("n not found", n); break; fi;
od: # od n
[seq(A[i], i=1..1000]; # N. J. A. Sloane, Oct 29 2020


CROSSREFS

Cf. A064413, A098550, A100113, A152248.
Sequence in context: A343144 A050005 A272026 * A253765 A077932 A272458
Adjacent sequences: A152244 A152245 A152246 * A152248 A152249 A152250


KEYWORD

nonn


AUTHOR

Leroy Quet, Nov 30 2008


EXTENSIONS

Extended by Ray Chandler, Dec 05 2008


STATUS

approved



