A352537 - OEIS

%I #9 Mar 20 2022 06:44:26

%S 2,3,919,1223,1699,3329,8009,11717,13691,19079,20921,21011,22643,

%T 22739,24623,26309,28571,28619,28979,30389,33629,34739,35257,41179,

%U 42577,48647,54133,58601,59627,61511,65171,70979,75707,80141,84221,86869,90677,93557,94781

%N Primes whose position in the Wythoff array is immediately followed by a prime both in the next column and the next row.

%e The Wythoff array begins:

%e    1    2    3    5   ...

%e    4    7   11   18   ...

%e    6   10   16   26   ...

%e    ...

%e where one can see these 2 patterns:

%e    2    3   and   3    5

%e    7             11

%e so 2 and 3 are terms.

%o (PARI) T(n,k) = (n+sqrtint(5*n^2))\2*fibonacci(k+1) + (n-1)*fibonacci(k); \\ A035513

%o cell(n) = for (r=1, oo, for (c=1, oo, if (T(r,c) == n, return([r, c])); if (T(r,c) > n, break);););

%o isokp(m) = my(pos = cell(prime(m))); isprime (T(pos[1], pos[2]+1)) && isprime(T(pos[1]+1, pos[2]));

%o lista(nn) = for (n=1, nn, if (isokp(n), print1(prime(n), ", ")));

%Y Cf. A003603, A035612, A035513 (Wythoff array).

%Y Intersection of A352538 and A352539.

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 20 2022