A255092 Least prime p such that p+n is product of (n+1) primes (with multiplicity).

2, 3, 43, 13, 239, 59, 171869, 569, 32797, 2551, 649529, 6133, 1708984363, 57331, 103630981, 65521, 301327031, 262127, 82244873046857, 11943917, 38354628391, 26214379, 679922958173, 37748713, 584125518798828101, 553648103, 7625597484961, 2281701349, 882592301503097, 8153726947

Offset: 0

Author

Zak Seidov, Feb 14 2015

Keywords

• nonn
• look

Comments

For n>0, terms with odd indices 3, 13, 59, 569... are much smaller than neighbor terms with even indices.

For n > 0, a(n) >= A053669(n)^(n+1) - n. - Robert Israel, Sep 25 2024

Examples

			2+0=2(prime), 3+1=4=2*2, 43+2=45=3*3*5, 13+3=16=2^4, 239+4=243=3^5,59+5=64=2^6,171869+6=171875=5^6*11,569+7=574=2^6*3^2,
32797+8=32805=3^5*5, 2551+9=2590=2^9*5, 649529+10=649539=3^10*11, 6133+11=6143=2^11*3.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A053669, A072875, A112998, A113000, A113008.

Programs

Maple

f:= proc(n)
    uses priqueue;
      local pq, t, v, p,w,i;
      initialize(pq);
      p:= 2;
      while n mod p = 0 do p:= nextprime(p) od;
      insert([-p^(n+1),[p$(n+1)]],pq);
      do
        t:= extract(pq);
        v:= -t[1]; w:= t[2];
        if isprime(v-n) then return v-n fi;
        p:= nextprime(w[-1]);
      while n mod p = 0 do p:= nextprime(p) od:
       for i from n+1 to 1 by -1 while w[i] = w[n+1] do
        insert([t[1]*(p/w[n+1])^(n+2-i),[op(w[1..i-1]),p$(n+2-i)]],pq);
     od od
end proc:
f(0):= 2:
map(f, [$0..40]); # Robert Israel, Sep 25 2024

Extensions

More terms from Robert Israel, Sep 25 2024