A365235 - OEIS

%I #31 Aug 30 2023 11:39:33

%S 2,19,29,59,71,79,101,131,149,151,191,251,281,331,379,389,401,449,461,

%T 499,509,521,569,571,599,641,659,691,739,761,811,919,971,991,1009,

%U 1019,1129,1151,1259,1321,1409,1511,1531,1559,1579,1601,1621,1669,1699,1811,1901,1931,1979,1999,2081,2141

%N Least increasing sequence of primes such that a(n-1)^2 + a(n)^2 is semiprime, with a(1)=2.

%C For n >= 2, a(n) == 1 or 9 (mod 10) and a(n)^2 + a(n+1)^2 is twice a prime.

%H Robert Israel, <a href="/A365235/b365235.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 19 because a(1) = 2 and 2^2 + 19^2 = 365 = 5 * 73 is a semiprime.

%e a(3) = 29 because 19^2 + 29^2 = 1202 = 2*601 is a semiprime.

%p R:= 2,19: b:= 19^2: p:= 19: count:= 2:

%p while count < 100 do

%p   p:= nextprime(p);

%p   if isprime((b+p^2)/2) then

%p     R:= R,p; count:= count+1; b:= p^2;

%p   fi

%p od:

%p R;

%t p = 3; s = {q = 2}; Do[While[2 != PrimeOmega[q^2 + p^2], p = NextPrime[p]]; AppendTo[s, q = p], {100}];s

%Y Cf. A001358.

%K nonn

%O 1,1

%A _Zak Seidov_ and _Robert Israel_, Aug 28 2023