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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
 1, 2, 3, 4, 6, 12, 211050, 3848880, 20333040, 125038830, 2978699430 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. LINKS EXAMPLE 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). PROG (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) CROSSREFS Cf. A030063, A034881, A246655. Sequence in context: A018698 A018738 A018765 * A096988 A066463 A073146 Adjacent sequences:  A274691 A274692 A274693 * A274695 A274696 A274697 KEYWORD nonn,more AUTHOR Robert C. Lyons, Jul 02 2016 STATUS approved

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Last modified July 30 03:31 EDT 2021. Contains 346347 sequences. (Running on oeis4.)