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(n-1)) > 1.

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

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[n-1]))};
  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