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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

Table of n, a(n) for n=1..11.

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.)