A357777 a(1)=1, a(2)=2. Thereafter a(n+1) is the smallest k such that gcd(k, a(n)) > 1, and gcd(k, s(n)) = 1, where s(n) is the n-th partial sum.

1, 2, 4, 6, 3, 9, 12, 8, 14, 7, 35, 5, 15, 10, 16, 20, 18, 21, 27, 24, 22, 11, 33, 30, 25, 55, 40, 26, 13, 39, 36, 28, 32, 34, 17, 51, 45, 57, 19, 133, 38, 44, 46, 23, 69, 42, 48, 50, 52, 54, 56, 49, 63, 60, 58, 29, 87, 66, 62, 31, 93, 72, 64, 68, 70, 65, 75, 78

Offset

1,2

Comments

Conjectured to be a permutation of the positive integers.

Links

Table of n, a(n) for n=1..68.

Michael De Vlieger, Log-log scatterplot of a(n), n = 1..2^14, labeling records in red, local minima in blue, highlighting prime terms in green, prime partial sums in gold and labeling those in orange italics.

Example

a(3) = 4 because 4 is the smallest number which has not occurred already which is prime to s(2)=3 and shares a divisor (2) with a(2)=2.

Mathematica

nn = 68; c[_] = False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; u = s = 3; Do[j = a[n - 1]; k = u; If[CoprimeQ[j, s], While[Nand[! c[k], CoprimeQ[k, s], ! CoprimeQ[j, k], k != s], k++]]; Set[{a[n], c[k]}, {k, True}]; s += k; If[k == u, While[c[u], u++]], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Oct 13 2022 *)

Crossrefs

Cf. A064413, A357735.

Sequence in context: A255348 A342366 A336946 * A348086 A122280 A365259

Adjacent sequences: A357774 A357775 A357776 * A357778 A357779 A357780

Keyword

nonn

Author

David James Sycamore, Oct 12 2022

Status

approved