A122090 a(1)=1. a(n) = smallest integer that is greater than a(n-1) and is coprime to the largest nonprime (1 or composite) occurring among the first (n-1) terms of the sequence.

1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 41, 43, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 71, 73, 79, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 101, 103, 107, 109, 113, 115, 116, 117

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Example

The smallest integer that is greater than a(20)=29 and is coprime to 28 (the largest nonprime which occurs among the first 20 terms of the sequence) is 31. So a(21) = 31.

Maple

A122090 := proc(maxn) local a, nexta, n, lanopr; a := [1]; lanopr := 1; for n from 2 to maxn do nexta := op(n-1, a)+1; while gcd(nexta, lanopr) >1 do nexta := nexta+1; od; a := [op(a), nexta]; if not isprime(nexta) and nexta > lanopr then lanopr := nexta; fi; od; RETURN(a); end: maxn := 100 : alist := A122090(maxn) : for i from 1 to maxn do printf("%d, ", op(i, alist)); end : # R. J. Mathar, Oct 21 2006

Mathematica

f[l_List] := Block[{k = Last[l] + 1, m = Max[Select[l, ! PrimeQ[ # ] &]]}, While[GCD[k, m] > 1, k++ ]; Append[l, k]]; Nest[f, {1}, 70] (* Ray Chandler, Oct 19 2006 *)

Crossrefs

Sequence in context: A228894 A325367 A160718 * A066050 A004050 A123538

Adjacent sequences: A122087 A122088 A122089 * A122091 A122092 A122093

Keyword

nonn

Author

Leroy Quet, Oct 17 2006

Extensions

Extended by Ray Chandler, Oct 19 2006

More terms from R. J. Mathar, Oct 21 2006

Status

approved