A345447 Numbers of the form i+j+2*i*j and 2+i+j+2*i*j for i,j >= 1.

4, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80

Offset: 1

Author

Davide Rotondo, Jun 19 2021

Keywords

• nonn

Comments

Except for 1 and 2 the complement sequence c is: 3, 5, 8, 11, 20, 23, 35, 41, 50, 53, 56, 65, ...; where 2*c(i) + 1 and 2*c(i) - 3 are a pair of cousin primes. This is a consequence of the sieve of Sundaram.

Examples

			For i,j = 1, 1+1+2*1*1 = 4 and 2+1+1+2*1*1 = 6.
		

Links

• Wikipedia, Sieve of Sundaram.

Crossrefs

Cf. A046132, A023200.

Union of A047845 and A153043, except for 0 and 2.

Programs

Python

def aupto(limit):
    aset = set()
    for i in range(1, limit//3):
        for j in range(i, limit//3):
            t = i + j + 2*i*j
            if t > limit: break
            aset.update([t, t+2])
    return sorted(an for an in aset if an <= limit)
print(aupto(80)) # Michael S. Branicky, Jul 05 2021