A387079 Least prime factor of A386482(n).

1, 2, 2, 2, 3, 3, 2, 2, 2, 2, 7, 3, 2, 2, 2, 3, 5, 5, 2, 2, 2, 2, 2, 11, 3, 3, 2, 2, 2, 2, 19, 3, 2, 2, 2, 2, 2, 2, 2, 2, 5, 3, 3, 13, 5, 2, 2, 2, 7, 3, 3, 17, 2, 2, 2, 2, 31, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 3, 3, 23, 2, 2, 47, 3, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Michael De Vlieger, Aug 18 2025

Keywords

• nonn

Comments

Minimum absolute difference |s(n-1)-s(n)|, since GCD(s(n-1),s(n)) > 1, where s = A386482.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020639, A386482, A387073, A387074, A387075.

Programs

Mathematica

Block[{c, j, k, p, m, nn}, nn = 120; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; {1, 2}~Join~Reap[Do[If[PrimePowerQ[j], Set[{p, k, m}, {#1, #1^(#2 - 1), #1^(#2 - 1)}] & @@ FactorInteger[j][[1]]; While[And[c[k*p], k != 0], k--];vIf[k == 0, k = m; While[c[k*p], k++]]; k *= p, k = j - 1; While[And[Or[c[k], CoprimeQ[j, k]], k != 1], k--]; If[k == 1, k += j; While[Or[c[k], CoprimeQ[j, k]], k++] ] ]; Sow[FactorInteger[k][[1, 1]] ]; Set[{c[k], j}, {True, k}], {n, 3, nn}]][[-1, 1]] ]

Formula

a(n) = A020639(A386482(n)).

a(n) <= |A386075(n-1)|.

a(m) = s(m) = A387073(i) for m = A387074(i).