A276458 Smallest odd number not of the form p + 2^k with p prime and k >= 0 that is divisible by the n-th prime.

1719, 905, 959, 1199, 1807, 1207, 2983, 1541, 2465, 1271, 5143, 1271, 2279, 1927, 2279, 1829, 5917, 1541, 1207, 2263, 3239, 7387, 4717, 1649, 6161, 4841, 7169, 1199, 1243, 127, 10873, 959, 1529, 149, 11023, 2669, 12877, 2171, 1211, 1969, 905, 1719, 7913, 7289

Offset: 2

Author

Arkadiusz Wesolowski, Sep 03 2016

Keywords

• nonn

Comments

a(n) <= A213529(n).

Examples

			a(3) = 905 because it is the smallest de Polignac number (A006285) divisible by the third prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..3000

Crossrefs

Cf. A006285, A098237, A213529.

Programs

Magma

lst:=[]; for r in [2..45] do p:=NthPrime(r); n:=-p; f:=0; while IsZero(f) do n:=n+2*p; k:=-1; repeat k+:=1; a:=n-2^k; until a lt 1 or IsPrime(a); if a lt 1 then Append(~lst, n); f:=1; end if; end while; end for; lst;

Maple

N:= 10^5: # to use de Polignac numbers <= N
P:= select(isprime,{2,seq(i,i=3..N,2)}):
dP:= {seq(i,i=1..N,2)}:
for k from 0 to ilog2(N) do
  dP:= dP minus map(`+`,P,2^k)
od:
for m from 2 do
   R:= ListTools:-SelectFirst(1, t -> t mod P[m] = 0, dP);
   if R = {} then break fi;
   A[m]:= R[1];
od:
seq(A[i],i=2..m-1); # Robert Israel, Sep 06 2016