

A274694


Variation on Fermat's Diophantine mtuple: 1 + the product of any two distinct terms is a prime power.


0



1, 2, 3, 4, 6, 12, 211050, 3848880, 20333040, 125038830, 2978699430
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OFFSET

1,2


COMMENTS

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.


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 = []
prev_element = 1
seq.append( prev_element )
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 = 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,changed


AUTHOR

Robert C. Lyons, Jul 02 2016


STATUS

approved



