A274694 Variation on Fermat's Diophantine m-tuple: 1 + the product of any two distinct terms is a prime power.

1, 2, 3, 4, 6, 12, 211050, 3848880, 20333040, 125038830, 2978699430

Offset: 1

Author

Robert C. Lyons, Jul 02 2016

Keywords

• nonn
• more

Comments

a(1) = 1; for n>1, a(n) = smallest integer > a(n-1) such that a(n)*a(i)+1 is a prime power for all 1 <= i <= n-1.

Examples

			After a(1)=1, a(2)=2, a(3)=3, we want m, the smallest number > 3 such that m+1, 2m+1 and 3m+1 are all prime powers: this is m = 4 = a(4).
		

Crossrefs

Cf. A030063, A034881, A246655.

Programs

Sage

seq = [1]
prev_element = 1
max_n = 8
for n in range(2, max_n+1):
    next_element = prev_element + 1
    while True:
        all_match = True
        for element in seq:
            x = element * next_element + 1
            if not x.is_prime_power():
                all_match = False
                break
        if all_match:
            seq.append( next_element )
            break
        next_element += 1
    prev_element = next_element
print(seq)