First 11 values of A121387 coincide with apparently unrelated new seq

Jonathan Post jvospost3 at gmail.com
Wed Jun 20 20:57:33 CEST 2007


The semiprime hypotenuses of my sequence must be the product of two odd primes.

a^2 + b^2 = (pq)^2 for odd primes p, q.

Whether two odd primes p and q are of the form 4n+1 or 4n+3, their
product, squared, must be of the form 4n+1.

a^2 + b^2 = 4n+1 forces exactly one of the legs a,b to be odd, and the
other to be a multiple of 4.  Hence no primitive Pythagorean triple
consists of 3 semiprimes.

Alford Arnold's sequence A121388 claims to have 5 subsequences:
A002145 Primes of the form 4n+3
A002144 Primes of the form 4n+1
A107978 Products of two primes of form 4n+3 (a seq of mine)
A080774 (4*i+1)*(4*j+3) = semiprimes of form 4n+1
A121387  "Fifth diagonal of A121388"????

What am I missing?





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