A361490 - OEIS

%I #8 Mar 14 2023 11:46:19

%S 8,45,52,75,92,99,130,147,164,195,236,255,266,333,406,423,430,477,494,

%T 555,574,627,670,711,716,777,782,801,806,903,908,915,932,935,938,969,

%U 1010,1017,1022,1065,1076,1233,1244,1443,1474,1479,1490,1533,1556,1635,1724,1737,1790,1833,1844,2007,2012

%N a(1) = 8; for n > 1, a(n) is the least triprime > a(n-1) such that a(n) - a(n-1) and a(n) + a(n-1) are both prime.

%C a(n) == n-1 (mod 2).

%H Robert Israel, <a href="/A361490/b361490.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 75 because 75 = 3*5^2 is a triprime > a(3) = 52, 75 - 52 = 23 and 75 + 52 = 127 are prime, and none of the earlier triprimes > 52 (63, 66, 68, 70) works.

%p A[1]:= 8:

%p for i from 2 to 100 do

%p   for x from A[i-1]+1 by 2 do

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

%p       A[i]:= x; break

%p     fi

%p od od:

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

%t s={8};m=8;Do[n = m + 1; While[3 != PrimeOmega[n] || ! PrimeQ[m + n] || ! PrimeQ[n - m], n++]; Print[m=n];AppendTo[s,m],{10}]

%Y Cf. A014612.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Mar 14 2023