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A274697 Variation on Fermat's Diophantine m-tuple: 1 + the GCD of any two distinct terms is a square. 0
0, 3, 15, 24, 48, 63, 120, 195, 255, 528, 960, 3024, 3363, 3480, 3720, 3843, 4095, 4623, 5475, 12099, 16383, 19599, 24963, 37635, 38415, 44943, 56643, 62499, 65535, 69168, 71823, 85263, 94863, 114243, 168099 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(1) = 0; for n>1, a(n) = smallest integer > a(n-1) such that GCD(a(n),a(i))+1 is square for all 1 <= i <= n-1.

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

After a(1)=0, a(2)=3, a(3)=15, we want m, the smallest number > 15 such that GCD(0,m)+1, GCD(3,m)+1 and GCD(15,m)+1 are squares: this is m = 24 = a(4).

PROG

(Sage)

seq = []

prev_element = 0

seq.append( prev_element )

max_n = 35

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

    next_element = prev_element + 1

    while True:

        all_match = True

        for element in seq:

            x = gcd( element, next_element ) + 1

            if not ( is_square(x) ):

                all_match = False

                break

        if all_match:

            seq.append( next_element )

            print(seq)

            break

        next_element = next_element + 1

    prev_element = next_element

print(seq)

CROSSREFS

Cf. A030063.

Sequence in context: A101133 A061386 A057780 * A129024 A018982 A276938

Adjacent sequences:  A274694 A274695 A274696 * A274698 A274699 A274700

KEYWORD

nonn

AUTHOR

Robert C. Lyons, Jul 05 2016

STATUS

approved

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Last modified September 24 11:16 EDT 2021. Contains 347642 sequences. (Running on oeis4.)