A075341 a(1) = 1, a(2n) is the smallest composite number == 1 mod (a(2n-1)) and a(2n+1) is the smallest prime == 1 (mod a(2n)).

1, 4, 5, 6, 7, 8, 17, 18, 19, 20, 41, 42, 43, 44, 89, 90, 181, 182, 547, 548, 1097, 1098, 7687, 7688, 15377, 15378, 30757, 30758, 276823, 276824, 553649, 553650, 2768251, 2768252, 8304757, 8304758, 99657097, 99657098, 199314197, 199314198

Offset: 1

Author

Amarnath Murthy, Sep 18 2002

Keywords

• nonn

Comments

a(k) = b(k-5) for k > 8 where b(r) is the r-th term of A075340.

Crossrefs

Cf. A075340.

See also: Always look for prime: A061092. Always look for composite: A061766.

Programs

Mathematica

a[1] = 1; a[2] = 4; a[n_] := a[n] = Block[{k = a[n - 1] + 1, m = a[n - 1]}, If[OddQ@n, While[ !PrimeQ@k || Mod[k, m] != 1, k += m]; k, While[PrimeQ@k || Mod[k, m] != 1, k += m]; k]]; Array[a, 40] (* Robert G. Wilson v Sep 21 2006 *)

Extensions

More terms from David Wasserman, Jan 16 2005