A365537 a(n) is the first semiprime k such that k-1 and k+1 each have exactly n prime factors (counted with multiplicity).

4, 34, 51, 55, 1169, 6641, 18751, 204929, 101249, 2490751, 6581249, 68068351, 262986751, 1842131969, 9601957889, 13858918399, 145046192129, 75389157377, 18444674957311, 39806020354049, 124758724247551, 878616032837633, 551785225781249

Offset

1,1

Comments

a(n) is the least k such that A001222(k) = 2 and A001222(k - 1) = A001222(k + 1) = n.

Links

Table of n, a(n) for n=1..23.

Example

a(3) = 51 because 51 = 3 * 17 is a semiprime and 50 - 1 = 50 = 2 * 5^2 and 51 + 1 = 52 = 2^2 * 13 are triprimes.

Maple

V:= Vector(10): count:= 0:
b:= 1: c:= 2:
for x from 5 while count < 10 do
  a:= b; b:= c; c:= numtheory:-bigomega(x);
  if b = 2 and a = c and V[a] = 0 then
    count:= count+1; V[a]:= x-1; printf("%d %d\n", a, x-1);
  fi
od:
convert(V, list);

Mathematica

seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 2, c = 0, m}, While[c < len && k < kmax, If[PrimeOmega[k] == 2, m = PrimeOmega[k - 1]; If[m <= len && s[[m]] == 0 && PrimeOmega[k + 1] == m, c++; s[[m]] = k]]; k++]; s]; seq[10, 10^7] (* Amiram Eldar, Sep 08 2023 *)

Crossrefs

Cf. A001222, A001358.

Sequence in context: A057959 A220168 A227397 * A281827 A284812 A053902

Adjacent sequences: A365534 A365535 A365536 * A365538 A365539 A365540

Keyword

nonn

Author

Zak Seidov and Robert Israel, Sep 08 2023

Extensions

a(14) from Amiram Eldar, Sep 08 2023

a(15)-a(23) from Martin Ehrenstein, Dec 26 2023

Status

approved