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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

%I #38 Apr 10 2023 01:41:00

%S 8,20,50,125,279,426,531,539,814,822,897,1002,1010,1076,1146,1209,

%T 1325,1353,1398,1406,1516,1558,1868,1898,1948,1978,1986,2013,2225,

%U 2233,2397,2527,2547,2575,2763,2783,2810,2908,2938,2946,3009,3054,3081,3414,3422,3452,3522,3567,3714,3759,3786,3813

%N 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.

%H Robert Israel, <a href="/A361073/b361073.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p A[1]:= 8:

%p for i from 2 to 100 do

%p for x from A[i-1]+8 do

%p if numtheory:-bigomega(x) = 3 and numtheory:-bigomega(x-A[i-1]) = 3 and numtheory:-bigomega(x+A[i-1]) = 3 then

%p A[i]:= x; break

%p fi

%p od od:

%p seq(A[i],i=1..100);

%t s = {m = 8}; Do[p = m + 8; While[{3, 3, 3} != PrimeOmega[{p, m + p,

%t p - m}], p++]; AppendTo[s, m = p], {50}]; s

%Y Cf. A014612, A361611, A361215.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Apr 09 2023