A381328 - OEIS

%I #11 Feb 23 2025 17:29:56

%S 0,1,4,8,17,28,52,83,142,232,377,614,996,1641,2642,4290,6945,11246,

%T 18198,29457,47662,77124,124797,201928,326736,528723,855464,1384230,

%U 2239797,3624050,5863850,9487911,15351768,24839684,40191555,65031270,105222856,170254137,275477064,445731218,721208325,1166939604

%N a(n+1) is the least k such that k - (a(n-1)+a(n)) and k + (a(n-1)+a(n)) are primes; a(0)=0, a(1)=1.

%H Robert Israel, <a href="/A381328/b381328.txt">Table of n, a(n) for n = 0..4759</a>

%e a(5) = 28 because a(3) + a(4) = 8 + 17 = 25, 28 - 25 = 3 and 28 + 25 = 53 are prime, and no smaller number works.

%p A[0]:= 0: A[1]:= 1:

%p for i from 2 to 50 do

%p   p:= 0;

%p   do

%p     p:= nextprime(p);

%p     if isprime(p + 2*(A[i-1]+A[i-2])) then

%p       A[i]:= p + A[i-1]+A[i-2];

%p       break

%p     fi

%p   od

%p od:

%p seq(A[j],j=0..50);

%t s={0,1};Do[k=s[[-1]]+s[[-2]];Until[PrimeQ[k-s[[-1]]-s[[-2]]]&&PrimeQ[k+s[[-1]]+s[[-2]]],k++];AppendTo[s,k],{n,40}];s (* _James C. McMahon_, Feb 21 2025 *)

%K nonn

%O 0,3

%A _Robert Israel_, Feb 20 2025