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

1,2

Comments

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

Links

Table of n, a(n) for n=1..40.

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 *)

Crossrefs

Cf. A075340.

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

Sequence in context: A274552 A280682 A140293 * A309358 A143789 A068521

Adjacent sequences: A075338 A075339 A075340 * A075342 A075343 A075344

Keyword

nonn

Author

Amarnath Murthy, Sep 18 2002

Extensions

More terms from David Wasserman, Jan 16 2005

Status

approved