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A187797
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.
9
10, 16, 18, 22, 24, 30, 34, 36, 42, 46, 48, 54, 60, 64, 66, 72, 76, 78, 84, 90, 102, 106, 108, 112, 114, 120, 126, 132, 138, 142, 144, 150, 154, 156, 162, 168, 174, 180, 184, 186, 192, 196, 198, 202, 204, 210, 216, 222, 228, 232, 234, 240, 244, 246, 252, 258, 264, 270, 274, 276, 282, 286
OFFSET
1,1
COMMENTS
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
EXAMPLE
For n=10, the partition solutions are 3+7 and 5+5, giving p=3, q=7, p+2=5, q-2=5.
MAPLE
isA187797 := proc(n)
local i, p, q ;
for i from 1 do
p := ithprime(i) ;
q := n-p ;
if q <= p+2 then
return false;
end if;
if isprime(q) then
if isprime(p+2) and isprime(q-2) then
return true;
end if;
end if;
end do:
return false;
end proc:
for n from 4 to 600 do
if isA187797(n) then
printf("%d, ", n);
end if;
end do: # R. J. Mathar, Oct 03 2013
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A103208 A323196 A352240 * A352297 A192221 A106695
KEYWORD
nonn
AUTHOR
Bob Gilson, Aug 30 2013
STATUS
approved