A113521 a(n) = largest nonprime nonnegative integer < c(n) which is coprime to c(n), where c(n) is the n-th composite positive integer.

1, 1, 1, 8, 9, 1, 9, 14, 15, 1, 9, 20, 21, 1, 24, 25, 26, 27, 1, 27, 32, 33, 34, 35, 35, 38, 39, 25, 39, 44, 45, 35, 48, 49, 50, 51, 49, 54, 55, 56, 57, 49, 57, 62, 63, 64, 65, 65, 68, 69, 65, 69, 74, 75, 76, 77, 77, 80, 81, 65, 84, 85, 86, 87, 77, 90, 91, 92, 93, 94, 95, 95, 98

Offset

1,4

Comments

a(n)=A002808(n)-1 if A002808(n)-1 is not prime. - Robert Israel, Dec 02 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 255 terms from Lior Manor)

Example

a(7) = 9 because 9 is the largest nonprime integer < 14 (the 7th composite) (since the other nonprime integers > 9 and < 14 {10 and 12} aren't coprime with 14).

Maple

N:=300:
NP:= remove(isprime, [$1..N]):
for i from 2 to nops(NP) do
  x:= NP[i];
  for k from i-1 by -1 do
    if igcd(NP[k], x) = 1 then A[i-1]:=NP[k]; break fi
  od
od:
seq(A[i], i=1..nops(NP)-1); # Robert Israel, Dec 02 2019

Mathematica

lnni[n_]:=Max[Select[Range[n-1], CompositeQ[#]&&CoprimeQ[#, n]&]]; lnni/@ Select[Range[200], CompositeQ]/.(-\[Infinity]->1) (* Harvey P. Dale, Jan 19 2019 *)

Crossrefs

Cf. A002808.

Sequence in context: A302765 A053463 A073636 * A297537 A030167 A010767

Adjacent sequences: A113518 A113519 A113520 * A113522 A113523 A113524

Keyword

nonn

Author

Leroy Quet, Jan 12 2006

Extensions

More terms from Lior Manor, Nov 21 2007

Status

approved