A274697 Variation on Fermat's Diophantine m-tuple: 1 + the GCD of any two distinct terms is a square.

0, 3, 15, 24, 48, 63, 120, 195, 255, 528, 960, 3024, 3363, 3480, 3720, 3843, 4095, 4623, 5475, 12099, 16383, 19599, 24963, 37635, 38415, 44943, 56643, 62499, 65535, 69168, 71823, 85263, 94863, 114243, 168099

Offset: 1

Author

Robert C. Lyons, Jul 05 2016

Keywords

• nonn

Comments

a(1) = 0; for n>1, a(n) = smallest integer > a(n-1) such that GCD(a(n),a(i))+1 is square for all 1 <= i <= n-1.

Examples

			After a(1)=0, a(2)=3, a(3)=15, we want m, the smallest number > 15 such that GCD(0,m)+1, GCD(3,m)+1 and GCD(15,m)+1 are squares: this is m = 24 = a(4).
		

Crossrefs

Cf. A030063.

Programs

Sage

seq = []
prev_element = 0
seq.append( prev_element )
max_n = 35
for n in range(2, max_n+1):
    next_element = prev_element + 1
    while True:
        all_match = True
        for element in seq:
            x = gcd( element, next_element ) + 1
            if not ( is_square(x) ):
                all_match = False
                break
        if all_match:
            seq.append( next_element )
            print(seq)
            break
        next_element = next_element + 1
    prev_element = next_element
print(seq)