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A274694 Variation on Fermat's Diophantine m-tuple: 1 + the product of any two distinct terms is a prime power. 0

%I

%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

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Last modified September 27 08:22 EDT 2021. Contains 347689 sequences. (Running on oeis4.)