A356825 a(n) is the least semiprime p*q such that p*q-i*(p+q) is prime for i from 1 to n but not n+1.

4, 9, 33, 65, 77, 161, 371, 38981, 2561, 568181

Offset

0,1

Comments

2*10^9 < a(10) <= 368470943651.

Links

Table of n, a(n) for n=0..9.

Example

a(3) = 65 = 5*13 because 65-18 = 47, 65-2*18 = 29, and 65-3*18 = 11 are prime but 65-4*18 = -7 is not, and 65 is the least semiprime that works.

Maple

V:= Array(0..9): V[0]:= 4: count:= 1:
for n from 9 by 2 while count < 10 do
   if numtheory:-bigomega(n) = 2 then
     P:= numtheory:-factorset(n);
     if nops(P) = 2 then s:= P[1]+P[2] else s:= 2*P[1] fi;
     for i from 1 while isprime(n-i*s) do od:
     v:=i-1;
     if V[v] = 0 then V[v]:= n; count:= count+1; fi
   fi
od:
convert(V, list);

Mathematica

primeQ[n_] := n > 0 && PrimeQ[n]; m[p_, q_] := Module[{i = 1}, While[primeQ[p*q - i*(p + q)], i++]; i]; seq[len_, nmax_] := Module[{s = Table[0, {len}], n = 1, c = 0, i, f}, While[c < len && n < nmax, f = FactorInteger[n]; If[f[[;; , 2]] == {2} || f[[;; , 2]] == {1, 1}, p = f[[1, 1]]; q = n/p; i = m[p, q]; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]]; n++]; s]; seq[10, 10^6] (* Amiram Eldar, Aug 29 2022 *)

Crossrefs

Cf. A001358, A356801.

Sequence in context: A320920 A368683 A048757 * A173659 A054433 A219769

Adjacent sequences: A356822 A356823 A356824 * A356826 A356827 A356828

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Aug 29 2022

Status

approved