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Primes whose position in the Wythoff array is immediately followed by another prime in the next row.
2

%I #13 Jan 25 2024 07:55:21

%S 2,3,13,17,59,71,101,157,347,359,401,683,821,881,919,1063,1223,1613,

%T 1699,1787,1931,2081,2333,2663,2711,2909,2999,3011,3299,3329,3371,

%U 3389,3623,3821,3911,4019,4049,4337,4349,4481,4931,5171,5273,5651,5741,5849,5879,6029,6079

%N Primes whose position in the Wythoff array is immediately followed by another prime in the next row.

%e The Wythoff array begins:

%e 1 2 3 5 8 13 ...

%e 4 7 11 18 29 47 ...

%e 6 10 16 26 42 68 ...

%e ...

%e So 2, 3 and 13 are terms since they are vertically followed by 7, 11 and 47.

%o (PARI)

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

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

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

%Y Cf. A352537 (next row and column), A352538 (next column).

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 20 2022