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

0,1

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

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A087571 A126018 A257467 * A237414 A051099 A162712

Adjacent sequences: A255089 A255090 A255091 * A255093 A255094 A255095

Keyword

nonn,look

Author

Zak Seidov, Feb 14 2015

Extensions

More terms from Robert Israel, Sep 25 2024

Status

approved