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A363594
a(n) = the n-th instance of b(k)/2 such that b(k-1) and b(k-2) are both odd, where b(n) = A359804(n).
2
2, 4, 8, 13, 16, 17, 19, 23, 26, 29, 31, 32, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 82, 83, 86, 89, 92, 94, 97, 101, 103, 106, 107, 109, 113, 116, 118, 122, 124, 127, 128, 131, 134, 136, 137, 139, 142, 146, 148, 149, 151, 152, 157, 158, 163, 164, 166, 167, 172
OFFSET
1,1
COMMENTS
The sequence strictly increases, a consequence of definition of A359804.
Conjecture: { A000079 \ {1} } U { A000040 \ {3, 5, 7, 11} } is a subset. In other words, this sequence is the union of powers of 2 greater than 1, and primes greater than 11.
This sequence is conjectured to be infinite. It tracks all occurrences of consecutive odd terms in A359804, which are (by definition) always followed by an even term, from which a(n) is derived. - David James Sycamore, Jun 21 2023
LINKS
FORMULA
a(n) = A359804(A363593(n)+2)/2 = A361639(A363593(n)+1).
EXAMPLE
a(1) = 2 since b(3..5) = {3, 5, 4}; 4/2 = 2.
a(2) = 4 since b(8..10) = {7, 9, 8}; 8/2 = 4.
a(3) = 8 since b(22..24) = {33, 35, 16}; 16/2 = 8.
a(4) = 13 since b(29..31) = {45, 49, 26}; 26/2 = 13.
a(5) = 16 since b(36..38) = {55, 63, 32}; 32/2 = 16, etc.
MATHEMATICA
nn = 500; c[_] = False; q[_] = 1;
Set[{i, j}, {1, 2}]; c[1] = c[2] = True; q[2] = 2; u = 3;
Reap[Do[
(k = q[#]; While[c[k #], k++]; k *= #;
While[c[# q[#]], q[#]++]) &[(p = 2;
While[Divisible[i j, p], p = NextPrime[p]]; p)];
If[OddQ[i j], Sow[k/2]];
Set[{c[k], i, j}, {True, j, k}];
If[k == u, While[c[u], u++]], {n, 3, nn}] ][[-1, -1]]
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved