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A361073
Lexicographically least increasing sequence of triprimes (A014612) a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also triprimes.
3
8, 20, 50, 125, 279, 426, 531, 539, 814, 822, 897, 1002, 1010, 1076, 1146, 1209, 1325, 1353, 1398, 1406, 1516, 1558, 1868, 1898, 1948, 1978, 1986, 2013, 2225, 2233, 2397, 2527, 2547, 2575, 2763, 2783, 2810, 2908, 2938, 2946, 3009, 3054, 3081, 3414, 3422, 3452, 3522, 3567, 3714, 3759, 3786, 3813
OFFSET
1,1
LINKS
EXAMPLE
a(3) = 50 because 50 = 2^2*5, 50 - a(2) = 30 = 2*3*5 and 50 + a(2) = 70 = 2*5*7 are all products of 3 (not necessarily distinct) primes, and 50 is the least number that works.
MAPLE
A[1]:= 8:
for i from 2 to 100 do
for x from A[i-1]+8 do
if numtheory:-bigomega(x) = 3 and numtheory:-bigomega(x-A[i-1]) = 3 and numtheory:-bigomega(x+A[i-1]) = 3 then
A[i]:= x; break
fi
od od:
seq(A[i], i=1..100);
MATHEMATICA
s = {m = 8}; Do[p = m + 8; While[{3, 3, 3} != PrimeOmega[{p, m + p,
p - m}], p++]; AppendTo[s, m = p], {50}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Apr 09 2023
STATUS
approved