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.

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

Author

Greg Knowles, Sep 15 2011

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A079545, A377791, A377882.

Programs

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 *)

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