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%I #8 Sep 24 2023 04:28:56
%S 4,22,29,37,79,106,154,172,191,211,254,326,352,379,466,529,667,704,
%T 904,947,991,1036,1129,1177,1276,1379,1486,1541,1597,1654,1712,1771,
%U 1892,1954,2279,2347,2557,2629,2776,2927,3004,3082,3161,3404,3571,3742,3829
%N Members of A000124 which are the arithmetic mean of two other members.
%e 4 = (1+7)/2, 37 = (7 +67)/2. etc.
%o (PARI) V = vector(5000); for (i = 1, 5000, V[i] = 1 + binomial(i, 2)); count = 0; i = 1; while (count < 50, i++; found = 0; j = i - 1; k = i + 1; x = 2*V[i]; while (!found && j, if (V[j] + V[k] > x, j--, if (V[j] + V[k] < x, k++, found = 1))); if (found, count++; print1(V[i], ", "))); \\ _David Wasserman_, Nov 18 2004
%Y Cf. A000124.
%K nonn
%O 1,1
%A _Amarnath Murthy_, May 05 2003
%E Corrected and extended by _David Wasserman_, Nov 18 2004
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