A358354 a(n) = n for n <= 3. Thereafter a(n) is the least m such that rad(m) = rad(rad(a(n-3)) + rad(a(n-1))) where rad is A007947.

1, 2, 3, 4, 8, 5, 7, 9, 16, 27, 6, 32, 25, 11, 13, 12, 17, 30, 18, 23, 53, 59, 82, 15, 74, 78, 93, 167, 35, 64, 169, 24, 128, 45, 21, 529, 38, 3481, 164, 60, 89, 57, 87, 22, 79, 166, 94, 173, 339, 433, 606, 105, 538, 286, 391, 929, 75, 406, 1335, 90, 218, 1553

Offset

1,2

Comments

Similar sequence to A358093, though here the definition works between a(n-1) and a(n-3) (skipping a(n-2)) so there is no evident parity pattern, and adjacent pairs are not always coprime.

Links

Table of n, a(n) for n=1..62.

Example

To find a(4): a(1)=1, a(3)=3 so a(4) is the least m such that rad(n) = rad(rad(1) + rad(3)) = rad(4) = 2. Since 2 has occurred already, a(4) = 4.

Mathematica

nn = 62; c[_] = False; p[_] = q[_] = 1; f[n_] := Times @@ FactorInteger[n][[All, 1]]; Array[Set[{a[#], c[#]}, {#, True}] &, 3]; Array[(q[#]++; p[#]++) &[f[a[#]] ] &, 3]; Set[{i, j, k}, Array[f[a[#]] &, 3]]; Do[s = f[i + k]; If[PrimeQ[s], m = s^p[s]; p[s]++, m = q[s]; While[Nand[! c[m s], PowerMod[s, s, m] == 0], m++]; m *= s]; q[s]++; Set[{a[n], c[m], i, j, k}, {m, True, j, k, s}], {n, 4, nn}]; Array[a, nn] (* Michael De Vlieger, Nov 12 2022 *)

Crossrefs

Cf. A007947, A358093.

Sequence in context: A246273 A082319 A082316 * A182513 A320504 A181799

Adjacent sequences: A358351 A358352 A358353 * A358355 A358356 A358357

Keyword

nonn

Author

David James Sycamore, Nov 11 2022

Status

approved