format for sending updates by email, was Re A093151

N. J. A. Sloane njas at
Thu May 31 20:00:54 CEST 2007

Dear Zak, I don't mind the sequence. I very much respect Neil's
keywording, even when he gives me a "less" or "dumb."

However, your "10" is rather arbitrary.  Since 10 is itself a
triangular number, I've submitted the slightly more general:


%I A000001
%S A000001 2, 3, 4, 1, 1, 7, 4, 1, 1, 7, 3
%N A000001 Least nonnegative m such that T(n) + T(m) is prime, for T(n)
= n(n+1)/2.
%C A000001 What is the simplest proof that this is defined for all
nonzero n?
%F A000001 a(n) = Min{m: m*(m+1)/2 + n*(n+1)/2 is prime}.
a(n) = Min{m: A000217(m) + A000217(n) is an element of A000040}.
%e A000001 a(6) = 4 because T(4) = 10 is the least triangular number
whose sum with T(6) = 21 is prime, since {21+0 = 3*7, 21+3 = 2^3*3, 21+6
= 3^3} are all composite, but 21+10 = 31 is prime.
%Y A000001 Cf. A000040, A000217, A129755, A130334.
%O A000001 0,1
%K A000001 ,easy,more,nonn,
%A A000001 Jonathan Vos Post (jvospost2 at, May 31 2007

Also, I feel your pain regarding email and password problems.  These
are curses of the late 20th and early 21st century.

An even more general sequence would be a table, by antidiagonals, of
the same but where "k-gonal number" replaces "triangular number." Yet
that does not inherently interest me, either, absent a nice proof or
asymptotic result.



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