This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309392 #13 Aug 16 2019 00:23:04
%S A309392 3,5,3,11,7,5,17,13,7,3,29,19,11,5,3,41,37,13,11,7,5,59,43,17,23,13,7,
%T A309392 3,71,67,23,29,19,11,5,3,101,79,31,53,31,17,17,7,5,107,97,37,59,37,19,
%U A309392 23,13,11,3,137,103,41,71,43,29,29,31,13,11,7,149,109
%N A309392 Square array read by downward antidiagonals: A(n, k) is the k-th prime p such that p + 2*n is also prime, or 0 if that prime does not exist.
%C A309392 The same as A231608 except that A231608 gives the upward antidiagonals of the array, while this sequence gives the downward antidiagonals.
%C A309392 Conjecture: All values are nonzero, i.e., for any even integer e there are infinitely many primes p such that p + e is also prime.
%C A309392 The conjecture is true if Polignac's conjecture is true.
%H A309392 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polignac%27s_conjecture">Polignac's conjecture</a>
%e A309392 The array starts as follows:
%e A309392 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191
%e A309392 3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193
%e A309392 5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73
%e A309392 3, 5, 11, 23, 29, 53, 59, 71, 89, 101, 131, 149, 173, 191
%e A309392 3, 7, 13, 19, 31, 37, 43, 61, 73, 79, 97, 103, 127, 139
%e A309392 5, 7, 11, 17, 19, 29, 31, 41, 47, 59, 61, 67, 71, 89
%e A309392 3, 5, 17, 23, 29, 47, 53, 59, 83, 89, 113, 137, 149, 167
%e A309392 3, 7, 13, 31, 37, 43, 67, 73, 97, 151, 157, 163, 181, 211
%e A309392 5, 11, 13, 19, 23, 29, 41, 43, 53, 61, 71, 79, 83, 89
%e A309392 3, 11, 17, 23, 41, 47, 53, 59, 83, 89, 107, 131, 137, 173
%e A309392 7, 19, 31, 37, 61, 67, 79, 109, 127, 151, 157, 211, 229, 241
%e A309392 5, 7, 13, 17, 19, 23, 29, 37, 43, 47, 59, 73, 79, 83
%o A309392 (PARI) row(n, terms) = my(i=0); forprime(p=1, , if(i>=terms, break); if(ispseudoprime(p+2*n), print1(p, ", "); i++))
%o A309392 array(rows, cols) = for(x=1, rows, row(x, cols); print(""))
%o A309392 array(12, 14) \\ Print initial 12 rows and 14 columns of the array
%Y A309392 Cf. A231608.
%Y A309392 Cf. A001359 (row 1), A023200 (row 2), A023201 (row 3), A023202 (row 4), A023203 (row 5), A046133 (row 6), A153417 (row 7), A049488 (row 8), A153418 (row 9), A153419 (row 10), A242476 (row 11), A033560 (row 12), A252089 (row 13), A252090 (row 14), A049481 (row 15), A049489 (row 16), A252091 (row 17), A156104 (row 18), A271347 (row 19), A271981 (row 20), A271982 (row 21), A272176 (row 22), A062284 (row 25), A049490 (row 32), A020483 (column 1).
%K A309392 nonn,tabl
%O A309392 1,1
%A A309392 _Felix Fröhlich_, Jul 28 2019