%I
%S 1,2,3,4,6,12,211050,3848880,20333040,125038830,2978699430
%N Variation on Fermat's Diophantine mtuple: 1 + the product of any two distinct terms is a prime power.
%C a(1) = 1; for n>1, a(n) = smallest integer > a(n1) such that a(n)*a(i)+1 is a prime power for all 1 <= i <= n1.
%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
