A246447 The odd primes squared plus 1 and the composites squared minus 1.

10, 15, 26, 35, 50, 63, 80, 99, 122, 143, 170, 195, 224, 255, 290, 323, 362, 399, 440, 483, 530, 575, 624, 675, 728, 783, 842, 899, 962, 1023, 1088, 1155, 1224, 1295, 1370, 1443, 1520, 1599, 1682, 1763, 1850, 1935, 2024, 2115, 2210, 2303, 2400, 2499, 2600

Offset: 1

Author

Leo Depuydt, Aug 26 2014

Keywords

• nonn
• easy

Comments

The odd primes squared plus 1 and the nonprimes squared minus 1 are the numerators or denominators of an infinite product converging to 1 whose denominators or numerators, conversely, are the squares of said numbers, that is, (p^2+1/p^2)*(q^2-1)/q^2)..., where p is an odd prime and q is a nonprime.

Union of A066872 and (A062312 - 1) with 0 and 5 removed. - Robert Israel, Aug 26 2014

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A066872, A062312.

Programs

PARI

lista(nn) = {for (n=3, nn, if (isprime(n), print1(n^2+1, ", "), print1(n^2-1, ", ")););} \\ Michel Marcus, Aug 26 2014

Python

for n in range(3,10**3):
  if isprime(n):
    print(n**2+1,end=', ')
  else:
    print(n**2-1,end=', ') # Derek Orr, Sep 19 2014

Extensions

More terms from Michel Marcus, Aug 26 2014