A274694 - OEIS

%I #11 Mar 14 2020 17:15:42

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

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

%C 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.

%e 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).

%o (Sage)

%o seq = [1]

%o prev_element = 1

%o max_n = 8

%o for n in range(2, max_n+1):

%o     next_element = prev_element + 1

%o     while True:

%o         all_match = True

%o         for element in seq:

%o             x = element * next_element + 1

%o             if not x.is_prime_power():

%o                 all_match = False

%o                 break

%o         if all_match:

%o             seq.append( next_element )

%o             break

%o         next_element += 1

%o     prev_element = next_element

%o print(seq)

%Y Cf. A030063, A034881, A246655.

%K nonn,more

%O 1,2

%A _Robert C. Lyons_, Jul 02 2016