A061766 -id:A061766 - cp's OEIS frontend

A131368 Coprime semiprimes: a(n-1) and a(n) are the closest coprime semiprimes.

4, 9, 10, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187, 194, 201, 202, 203

Offset: 1

Zak Seidov, Sep 30 2007

nonn

The slowest increasing sequence of semiprimes with coprime neighbor terms.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A051884, A061766, A107621, A109412.

Subsequence of A001358 (semiprimes).

A[1]:= 4: t:= 4: count:= 1:
for x from 5 while count < 100 do
  if igcd(x, t) = 1 then
    if numtheory:-bigomega(x)=2 then
      count:= count+1;
      A[count]:= x;
      t:= x;
    fi
  fi
od:
seq(A[i], i=1..100); # Robert Israel, Jun 11 2023

lista(nn) = {my(vsp = select((x->(bigomega(x) == 2)), vector(nn, k, k)), i = 1, last); while (i <= #vsp, print1(vsp[i], ", "); last = vsp[i]; while(gcd(vsp[i], last) != 1, i++; if (i>#vsp, break)););} \\ Michel Marcus, Jun 25 2019

gcd(a(n-1), a(n)) = 1.

A071258 a(1) = 4; a(n) = smallest composite number of form k*a(n-1) + 1 with k > 1.

Original entry on oeis.org

4, 9, 28, 57, 115, 231, 694, 1389, 2779, 5559, 16678, 33357, 66715, 133431, 400294, 800589, 1601179, 3202359, 9607078, 19214157, 38428315, 76856631, 153713263, 307426527, 614853055, 1229706111, 3689118334, 7378236669, 14756473339

Offset: 0

Amarnath Murthy, May 30 2002

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A061766, A061092, A059411.

nxt[n_]:=Module[{k=2},While[PrimeQ[k*n+1],k++];k*n+1]; NestList[nxt,4,30] (* Harvey P. Dale, Mar 26 2014 *)

More terms from Vladeta Jovovic, Jun 03 2002

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)).

Original entry on oeis.org

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

Amarnath Murthy, Sep 18 2002

nonn

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

Cf. A075340.

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

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 *)

More terms from David Wasserman, Jan 16 2005

cp's OEIS Frontend

A131368 Coprime semiprimes: a(n-1) and a(n) are the closest coprime semiprimes.

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A071258 a(1) = 4; a(n) = smallest composite number of form k*a(n-1) + 1 with k > 1.

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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)).

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