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A365145
Lexicographically least increasing sequence of triprimes (A014612) whose first differences are triprimes.
1
8, 20, 28, 70, 78, 98, 110, 130, 138, 165, 195, 207, 273, 285, 363, 426, 434, 442, 470, 498, 506, 518, 530, 548, 556, 574, 582, 590, 598, 606, 618, 638, 646, 654, 682, 710, 722, 730, 742, 754, 762, 782, 790, 834, 854, 874, 892, 942, 962, 970, 978, 986, 994, 1002, 1010, 1022, 1030, 1038, 1058
OFFSET
1,1
COMMENTS
a(n) - a(n-1) >= 8. If a(n-1) = 4*p where p is in A001359 then a(n) - a(n-1) = 8.
LINKS
EXAMPLE
a(2) = 20, a(3) = 28 = 2^2 * 7 is a triprime and 28 - 20 = 8 = 2^3 is a triprime, and this is the least number > 20 that works, so a(4) = 28.
MAPLE
R:= 8: m:= 8: count:= 1:
for t from 9 while count < 100 do
if numtheory:-bigomega(t) = 3 and numtheory:-bigomega(t-m) = 3 then
R:= R, t; m:= t; count:= count+1
fi
od:
R;
MATHEMATICA
Do[n = m + 8; While[{3, 3} != PrimeOmega[{n, n - m}],
n++]; AppendTo[s, m = n], {100}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Aug 23 2023
STATUS
approved