login
A194627
a(1)=1, a(n+1) = p(n)^2 + q(n)^2 + 1, where p(n) and q(n) are the number of prime and nonprime numbers respectively in the sequence so far.
3
1, 2, 3, 6, 9, 14, 21, 30, 41, 46, 59, 66, 81, 98, 117, 138, 161, 186, 213, 242, 273, 306, 341, 378, 417, 458, 501, 546, 593, 602, 651, 702, 755, 810, 867, 926, 987, 1050, 1115, 1182, 1251, 1322, 1395, 1470, 1547, 1626, 1707, 1790, 1875, 1962, 2051, 2142
OFFSET
1,2
LINKS
EXAMPLE
For n=1, we have no primes and one nonprime (a(1)=1), so a(2)=0^2+1^2+1=2. Now we have one prime (a(2)=2) and one nonprime, so a(3)=1^2+1^2+1=3.
MAPLE
R:= 1: v:= 1: p:= 0: q:= 0:
for i from 2 to 100 do
if isprime(v) then p:= p+1 else q:= q+1 fi;
v:= p^2 + q^2 + 1;
R:= R, v
od:
R; # Robert Israel, Nov 10 2024
MATHEMATICA
t = {1}; Do[ps = Count[t, _?(PrimeQ[#] &)]; AppendTo[t, ps^2 + (n - ps - 1)^2 + 1], {n, 2, 100}]; t (* T. D. Noe, Sep 15 2011 *)
PROG
(PARI) p=q=0; for(n=1, 50, print1(k=p^2+q^2+1", "); if(isprime(k), p++, q++)) \\ Charles R Greathouse IV, Sep 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Knowles, Sep 15 2011
STATUS
approved