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 A383134 #12 Apr 18 2025 09:53:25
%S A383134 2,1,1,2,3,1,1,1,2,1,2,3,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,5,1,1,1,
%T A383134 2,1,2,3,1,3,1,2,1,1,1,1,1,2,1,4,1,1,1,1,1,2,3,1,1,1,2,1,2,1,2,1,1,1,
%U A383134 1,1,2,1,3,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1
%N A383134 Array read by ascending antidiagonals: A(n,k) is the length of the arithmetic progression of only primes having difference n and first term prime(k).
%D A383134 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 139.
%F A383134 A(A006512(n),k) = 1 for n > 1.
%F A383134 A(A040976(n),k) = A054977(k+1).
%e A383134 The array begins as:
%e A383134 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A383134 1, 3, 2, 1, 2, 1, 2, 1, 1, 2, ...
%e A383134 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A383134 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, ...
%e A383134 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A383134 1, 1, 5, 3, 4, 2, 3, 1, 2, 1, ...
%e A383134 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A383134 1, 3, 2, 1, 2, 1, 1, 1, 2, 2, ...
%e A383134 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A383134 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, ...
%e A383134 ...
%e A383134 A(2,2) = 3 since 3 primes are in arithmetic progression with a difference of 2 and the first term equal to the 2nd prime: 3, 5, and 7.
%e A383134 A(6,3) = 5 since 5 primes are in arithmetic progression with a difference of 6 and the first term equal to the 3rd prime: 5, 11, 17, 23, and 29.
%t A383134 A[n_,k_]:=Module[{count=1,sum=Prime[k]},While[PrimeQ[sum+=n], count++]; count]; Table[A[n-k+1,k],{n,13},{k,n}]//Flatten
%Y A383134 Cf. A000012, A006512, A040976, A054977, A175191 (n=2).
%Y A383134 Cf. A088430, A206045, A237453.
%K A383134 nonn,tabl
%O A383134 1,1
%A A383134 _Stefano Spezia_, Apr 17 2025