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

1,2

Links

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

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

Cf. A079545, A377791, A377882.

Sequence in context: A325866 A094055 A094056 * A320595 A227564 A173303

Adjacent sequences: A194624 A194625 A194626 * A194628 A194629 A194630

Keyword

nonn,easy

Author

Greg Knowles, Sep 15 2011

Status

approved