A187797 - OEIS

%I #26 Feb 01 2021 18:29:49

%S 10,16,18,22,24,30,34,36,42,46,48,54,60,64,66,72,76,78,84,90,102,106,

%T 108,112,114,120,126,132,138,142,144,150,154,156,162,168,174,180,184,

%U 186,192,196,198,202,204,210,216,222,228,232,234,240,244,246,252,258,264,270,274,276,282,286

%N Numbers having at least two different ordered partitions p+q and (p+2)+(q-2) where p, q, p+2 and q-2 are all prime.

%C Numbers k with at least one pair of externally tangent circles with radius sqrt(2) and center (p,q) where p and q are prime, p + q = k and p <= q. - _Wesley Ivan Hurt_, Aug 11 2020

%e For n=10, the partition solutions are 3+7 and 5+5, giving p=3, q=7, p+2=5, q-2=5.

%p isA187797 := proc(n)

%p     local i,p,q ;

%p     for i from 1 do

%p         p := ithprime(i) ;

%p         q := n-p ;

%p         if q <= p+2 then

%p             return false;

%p         end if;

%p         if isprime(q) then

%p             if isprime(p+2) and isprime(q-2) then

%p                 return true;

%p             end if;

%p         end if;

%p     end do:

%p     return false;

%p end proc:

%p for n from 4 to 600 do

%p     if isA187797(n) then

%p         printf("%d,",n);

%p     end if;

%p end do: # _R. J. Mathar_, Oct 03 2013

%t Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]) (PrimePi[i + 2] - PrimePi[i + 1]) (PrimePi[2 n - i - 2] - PrimePi[2 n - i - 3]), {i, n - 2}] > 0, 2 n, {}], {n, 100}] // Flatten (* _Wesley Ivan Hurt_, Apr 13 2020 *)

%K nonn

%O 1,1

%A _Bob Gilson_, Aug 30 2013