cp's OEIS Frontend

A354087 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) and whose binary expansion has a single 1-bit in common with the binary expansion of a(n-1).

%I A354087 #11 Jul 14 2022 22:39:26
%S A354087 1,3,6,2,10,8,12,4,14,18,15,20,5,25,35,21,9,24,16,22,11,33,27,48,26,
%T A354087 13,52,32,34,30,36,28,7,42,49,77,56,38,19,133,57,69,46,66,39,65,45,50,
%U A354087 40,54,68,44,70,58,72,60,74,64,76,80,55,88,96,51,78,81,102,130,62,132,63,129,43,86,104,82
%N A354087 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) and whose binary expansion has a single 1-bit in common with the binary expansion of a(n-1).
%C A354087 This sequence is similar to the EKG sequence A064413 with the additional restriction that each term must share a single 1-bit in common with the previous term in their binary expansions. These restrictions lead to numerous terms being significantly larger than their preceding term, while the smaller terms overall show similar behavior to A109812. See the linked image. Unlike A064413 the primes do not occur in their natural order and both the proceeding and following terms of the primes can be large multiples of the prime.
%C A354087 In the first 100000 terms the fixed points are 1, 3, 30, 38, 350, 1603, 1936, 10176, 11976, 46123, 58471, 89870, although it is likely more exist. In the same range the lowest unseen number is 1019; the sequence is conjectured to be a permutation of the positive integers.
%H A354087 Scott R. Shannon, <a href="/A354087/a354087.png">Image of the first 100000 terms for values less than 200000</a>. The green line is y = n.
%e A354087 a(6) = 8 as a(5) = 10, 8 = 1000_2, 10 = 1010_2, and 8 is the smallest unused number that shares a common factor with 10 and has a single 1-bit in common with 10 in their binary expansions. Note that 4 satisfies the first criterion but not the second.
%Y A354087 Cf. A353989, A064413, A353245, A152458, A353712, A352633.
%K A354087 nonn,base
%O A354087 1,2
%A A354087 _Scott R. Shannon_, May 17 2022