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 A378288 #24 Nov 27 2024 18:58:32 %S A378288 1,2,1,3,3,1,5,5,2,1,6,9,7,3,1,9,15,10,5,2,1,13,27,11,9,3,7,3,18,45, %T A378288 13,15,6,17,6,1,19,59,14,45,9,41,13,3,2,26,211,25,61,11,101,125,7,5, %U A378288 13,43,303,62,65,13,157,150,9,11,27,3,46,425,70,227,23,367,195,11,14,43,14,11 %N A378288 Array read by antidiagonals: row k consists of the positive integers j for which the concatenation of 2^k - 1 and 2^j - 1 is prime. %C A378288 No terms are divisible by 4. %C A378288 All terms in row k are coprime to k. %C A378288 Conjecture: all rows have infinitely many terms, and all positive integers not divisible by 4 appear in infinitely many rows. %C A378288 k - 1 is in row k iff k is in A301806. %e A378288 The array starts %e A378288 1 2 3 5 6 9 13 18 ... %e A378288 1 3 5 9 15 27 45 59 ... %e A378288 1 2 7 10 11 13 14 25 ... %e A378288 1 3 5 9 15 45 61 65 ... %e A378288 1 2 3 6 9 11 13 23 ... %e A378288 1 7 17 41 101 157 367 571 ... %e A378288 3 6 13 125 150 195 634 1282 ... %e A378288 1 3 7 9 11 23 27 39 ... %e A378288 a(3,4) = 10 is a term in row 3 because the concatenation of 2^3 - 1 = 7 and 2^10 - 1 = 1023 is 71023, which is prime. %p A378288 tcat:= (a,b) -> 10^(1+ilog10(b))*a+b: %p A378288 N:= 8: # for the top left N x N array %p A378288 M:= Matrix(N, N): %p A378288 for i from 1 to N do %p A378288 count:= 0: %p A378288 x:= 2^i-1; %p A378288 for j from 1 by `if`(i::even,2,1) while count + i < N do %p A378288 if j mod 4 = 0 or igcd(i,j) > 1 then next fi; %p A378288 if isprime(tcat(x,2^j-1)) then count:= count+1; M[i,count]:= j fi; %p A378288 od; %p A378288 od: %p A378288 M; %p A378288 seq(seq(M[k,1+d-k], k=1..d), d=1..N-1); %Y A378288 Cf. A000225, A301806. %K A378288 nonn,base,tabl %O A378288 1,2 %A A378288 _Robert Israel_, Nov 26 2024