A178102 2^(absolute difference between prime factors of n-th semiprime) mod (n-th semiprime).

1, 2, 1, 8, 4, 4, 16, 6, 1, 20, 25, 26, 4, 10, 10, 12, 1, 13, 9, 43, 44, 16, 61, 52, 56, 16, 62, 16, 22, 22, 64, 70, 24, 44, 80, 28, 59, 30, 72, 1, 92, 31, 97, 106, 34, 106, 36, 4, 136, 110, 64, 40, 40, 9, 42, 1, 133, 134, 46, 81, 64, 146, 151, 152, 121

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 16 2010

Keywords

• nonn
• look

Comments

From Robert Israel, Apr 05 2020: (Start)

If A001358(n) = 2*p, then a(n) = (p+1)/2 if p == 3 (mod 4), or (3*p+1)/2 if p == 1 (mod 4).

If A001358(n) = 3*p with p > 3, then a(n) = (3*p+1)/4 if p == 1 (mod 4), or (9*p+1)/4 if p == 3 (mod 4). (End)

Examples

			a(1)=1 because the first semiprime is 4=2*2 and 2^(2-2) mod 4 = 1.
a(11)=25 because the 11th semiprime is 33=3*11 and 2^(11-3) mod 33 = 25.
		

Links

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

Crossrefs

Cf. A000079, A001358.

Programs

Maple

b:= proc(n) option remember;
  local k;
  if n=1 then 4
         else for k from b(n-1)+1 while
                  isprime(k) or add (i[2], i=ifactors(k)[2])<>2
              do od; k
  fi
end:
a:= proc(n)
  local l;
  l:= ifactors (b(n))[2];
  if nops (l)=1 then 1
  else 2 &^ abs(l[1][1]-l[2][1]) mod b(n)
  fi
end:
seq (a(n), n=1..65);

Mathematica

Mod[2^Differences[FactorInteger[#][[All,1]]],#]&/@Select[Range[300], PrimeOmega[ #] == 2&]/.{}->1//Flatten (* Harvey P. Dale, Dec 25 2018 *)

Extensions

Edited by Alois P. Heinz, Dec 17 2010