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 A247093 #118 Jun 08 2015 02:20:50
%S A247093 3,3,3,0,0,3,3,5,13,3,3,0,0,0,5,5,3,3,5,3,3,3,0,3,0,19,0,7,0,3,0,0,3,
%T A247093 0,3,7,19,0,3,0,0,0,31,0,3,17,5,3,3,5,3,5,7,5,3,3,0,0,0,3,0,3,0,0,0,3,
%U A247093 5,3,7,5,5,3,7,3,3,251,3,17,3,0,5,0,151,0,0,0,59,0,5,0,3,3,5,0,1097,0,0,3,3,0,0,7,0,17,3
%N A247093 Triangle read by rows: T(m,n) = smallest odd prime p such that (m^p-n^p)/(m-n) is prime (0<n<m), or 0 if no such p exists.
%C A247093 T(m,n) is 0 if and only if m and n are not coprime or A052409(m) and A052409(n) are not coprime. (The latter has some exceptions, like T(8,1) = 3. In fact, if p is a prime and does not equal to A052410(gcd(A052409(m),A052409(n))), then (m^p-n^p)/(m-n) is composite, so if it is not 0, then it is A052410(gcd(A052409(m),A052409(n))).) - _Eric Chen_, Nov 26 2014
%C A247093 a(i) = T(m,n) corresponds only to probable primes for (m,n) = {(15,4), (18,1), (19,18), (31,6), (37,22), (37,25), ...} (i={95, 137, 171, 441, 652, 655, ...}). With the exception of these six (m,n), all corresponding primes up to a(663) are definite primes. - _Eric Chen_, Nov 26 2014
%C A247093 a(n) is currently known up to n = 663, a(664) = T(37, 34) > 10000. - _Eric Chen_, Jun 01 2015
%C A247093 For n up to 1000, a(n) is currently unknown only for n = 664, 760, and 868. - _Eric Chen_, Jun 01 2015
%H A247093 Eric Chen, <a href="/A247093/b247093.txt">Table of n, a(n) for n = 1..663</a>
%H A247093 Eric Chen, <a href="/A247093/a247093_1.txt">Table of n, a(n) for n = 1..1000 status</a>
%e A247093 Read by rows:
%e A247093 m\n 1 2 3 4 5 6 7 8 9 10 11
%e A247093 2 3
%e A247093 3 3 3
%e A247093 4 0 0 3
%e A247093 5 3 5 13 3
%e A247093 6 3 0 0 0 5
%e A247093 7 5 3 3 5 3 3
%e A247093 8 3 0 3 0 19 0 7
%e A247093 9 0 3 0 0 3 0 3 7
%e A247093 10 19 0 3 0 0 0 31 0 3
%e A247093 11 17 5 3 3 5 3 5 7 5 3
%e A247093 12 3 0 0 0 3 0 3 0 0 0 3
%e A247093 etc.
%t A247093 t1[n_] := Floor[3/2 + Sqrt[2*n]]
%t A247093 m[n_] := Floor[(-1 + Sqrt[8*n-7])/2]
%t A247093 t2[n_] := n-m[n]*(m[n]+1)/2
%t A247093 b[n_] := GCD @@ Last /@ FactorInteger[n]
%t A247093 is[m_, n_] := GCD[m, n] == 1 && GCD[b[m], b[n]] == 1
%t A247093 Do[k=2, If[is[t1[n], t2[n]], While[ !PrimeQ[t1[n]^Prime[k] - t2[n]^Prime[k]], k++]; Print[Prime[k]], Print[0]], {n, 1, 663}] (* _Eric Chen_, Jun 01 2015 *)
%o A247093 (PARI) a052409(n) = my(k=ispower(n)); if(k, k, n>1);
%o A247093 a(m, n) = {if (gcd(m,n) != 1, return (0)); if (gcd(a052409(m), a052409(n)) != 1, return (0)); forprime(p=3,, if (isprime((m^p-n^p)/(m-n)), return (p)););}
%o A247093 tabl(nn) = {for (m=2, nn, for(n=1, m-1, print1(a(m,n), ", ");); print(););} \\ _Michel Marcus_, Nov 19 2014
%o A247093 (PARI) t1(n)=floor(3/2+sqrt(2*n))
%o A247093 t2(n)=n-binomial(floor(1/2+sqrt(2*n)), 2)
%o A247093 b(n)=my(k=ispower(n)); if(k, k, n>1)
%o A247093 a(n)=if(gcd(t1(n),t2(n)) !=1 || gcd(b(t1(n)), b(t2(n))) !=1, 0, forprime(p=3,2^24,if(ispseudoprime((t1(n)^p-t2(n)^p)/(t1(n)-t2(n))), return(p)))) \\ _Eric Chen_, Jun 01 2015
%Y A247093 Cf. A128164 (n,1), A125713 (n+1,n), A125954 (2n+1,2), A122478 (2n+1,2n-1).
%Y A247093 Cf. A000043 (2,1), A028491 (3,1), A057468 (3,2), A059801 (4,3), A004061 (5,1), A082182 (5,2), A121877 (5,3), A059802 (5,4), A004062 (6,1), A062572 (6,5), A004063 (7,1), A215487 (7,2), A128024 (7,3), A213073 (7,4), A128344 (7,5), A062573 (7,6), A128025 (8,3), A128345 (8,5), A062574 (8,7), A173718 (9,2), A128346 (9,5), A059803 (9,8), A004023 (10,1), A128026 (10,3), A062576 (10,9), A005808 (11,1), A210506 (11,2), A128027 (11,3), A216181 (11,4), A128347 (11,5), A062577 (11,10), A004064 (12,1), A128348 (12,5), A062578 (12,11).
%K A247093 nonn,tabl
%O A247093 1,1
%A A247093 _Eric Chen_, Nov 18 2014