A352538 Primes whose position in the Wythoff array is immediately followed by another prime in the next column.

2, 3, 7, 19, 23, 29, 67, 97, 103, 107, 149, 181, 227, 271, 311, 353, 379, 433, 449, 563, 631, 719, 761, 883, 919, 941, 971, 997, 1049, 1087, 1223, 1291, 1297, 1427, 1447, 1453, 1531, 1601, 1627, 1699, 1753, 1831, 1861, 1877, 2039, 2207, 2213, 2239, 2269, 2281, 2287

Offset: 1

Author

Michel Marcus, Mar 20 2022

Keywords

• nonn

Examples

			The Wythoff array begins:
   1    2    3    5    8 ...
   4    7   11   18   29 ...
   6   10   16   26   42 ...
   ...
So 2, 3 and 7 are terms, since they are horizontally followed by 3, 5 and 11.
		

Crossrefs

Cf. A003603, A022342, A035612, A035513 (Wythoff array).

Cf. A352537 (next row and column), A352539 (next row).

Programs

PARI

T(n,k) = (n+sqrtint(5*n^2))\2*fibonacci(k+1) + (n-1)*fibonacci(k); \\ A035513
cell(n) = for (r=1, oo, for (c=1, oo, if (T(r,c) == n, return([r, c])); if (T(r,c) > n, break);););
isokh(m) = {my(pos = cell(prime(m))); isprime (T(pos[1], pos[2]+1))};
lista(nn) = for (n=1, nn, if (isokh(n), print1(prime(n), ", ")));

PARI

right(n) = n++; (sqrtint(5*n^2)+n-2)\2; \\ see A022342
isokh(n) = isprime(right(n));
lista(nn) = for (n=1, nn, my(p=prime(n)); if (isokh(p), print1(p, ", ")));