A377882 -id:A377882 - cp's OEIS frontend

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

Greg Knowles, Sep 15 2011

			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.

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

Cf. A079545, A377791, A377882.

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

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 *)

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

A377791 Primes in A194627.

Original entry on oeis.org

2, 3, 41, 59, 593, 4787, 4937, 8699, 9281, 9491, 44201, 45491, 49429, 59219, 90197, 93251, 93893, 115211, 118661, 136523, 152501, 156467, 166949, 184571, 185477, 189851, 225353, 232091, 236981, 239963, 277577, 364571, 375569, 386731, 428873, 577307, 581941, 662339, 717161, 718931, 758501, 763811

Offset: 1

Robert Israel, Nov 10 2024

nonn

			a(3) = 41 because the third prime in A194627 is A194627(9) = 41.

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

Cf. A194627, A377882.

v:= 1: p:= 0: q:= 0: np:= 0: R:= NULL:
for i from 1 while np < 100 do
  if isprime(v) then p:= p+1; R:= R, v; np:= np+1 else q:= q+1 fi;
  v:= p^2 + q^2 + 1;
od:
R;

a(n) = A194627(A377882(n)).

a(n) = (n-1)^2 + (A377882(n)-n)^2 + 1.

cp's OEIS Frontend

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.

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