cp's OEIS Frontend

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

%I A352538 #19 Dec 26 2024 08:33:06
%S A352538 2,3,7,19,23,29,67,97,103,107,149,181,227,271,311,353,379,433,449,563,
%T A352538 631,719,761,883,919,941,971,997,1049,1087,1223,1291,1297,1427,1447,
%U A352538 1453,1531,1601,1627,1699,1753,1831,1861,1877,2039,2207,2213,2239,2269,2281,2287
%N A352538 Primes whose position in the Wythoff array is immediately followed by another prime in the next column.
%e A352538 The Wythoff array begins:
%e A352538    1    2    3    5    8 ...
%e A352538    4    7   11   18   29 ...
%e A352538    6   10   16   26   42 ...
%e A352538    ...
%e A352538 So 2, 3 and 7 are terms, since they are horizontally followed by 3, 5 and 11.
%o A352538 (PARI) T(n,k) = (n+sqrtint(5*n^2))\2*fibonacci(k+1) + (n-1)*fibonacci(k); \\ A035513
%o A352538 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 A352538 isokh(m) = {my(pos = cell(prime(m))); isprime (T(pos[1], pos[2]+1))};
%o A352538 lista(nn) = for (n=1, nn, if (isokh(n), print1(prime(n), ", ")));
%o A352538 (PARI) right(n) = n++; (sqrtint(5*n^2)+n-2)\2; \\ see A022342
%o A352538 isokh(n) = isprime(right(n));
%o A352538 lista(nn) = for (n=1, nn, my(p=prime(n)); if (isokh(p), print1(p, ", ")));
%Y A352538 Cf. A003603, A022342, A035612, A035513 (Wythoff array).
%Y A352538 Cf. A352537 (next row and column), A352539 (next row).
%K A352538 nonn
%O A352538 1,1
%A A352538 _Michel Marcus_, Mar 20 2022