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 A244740 Irregular triangular array read by rows:  T(n,k) = number of positive integers m such that (prime(n) mod m) = k, for k=1..(-1 + prime(k))/2. 4
 1, 2, 1, 3, 1, 1, 3, 2, 2, 1, 1, 5, 1, 2, 1, 1, 1, 4, 3, 2, 1, 2, 1, 1, 1, 5, 1, 3, 2, 2, 1, 1, 1, 1, 3, 3, 4, 1, 3, 1, 2, 1, 1, 1, 1, 5, 3, 2, 2, 4, 1, 2, 1, 2, 1, 1, 1, 1, 1, 7, 1, 4, 2, 2, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 8, 3, 2, 2, 3, 1, 3, 1, 2, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS (sum of numbers in row n) = prime(n+1)-2; (column 1) = A244796; (column 2) = A244797; (column 3) = A244798. LINKS Clark Kimberling, Table of n, a(n) for n = 1..500 EXAMPLE First 12 rows: 1 2 1 3 1 1 3 2 2 1 1 5 1 2 1 1 1 4 3 2 1 2 1 1 1 5 1 3 2 2 1 1 1 1 3 3 4 1 3 1 2 1 1 1 5 3 2 2 4 1 2 1 2 1 1 1 1 1 7 1 4 2 2 1 3 1 2 1 1 1 1 1 1 8 3 2 2 3 1 3 1 2 1 2 1 1 1 1 1 1 1 7 3 2 1 5 2 2 2 2 1 2 1 2 1 1 1 1 1 1 1 For row 4, count these congruences: 11 = (1 mod m) for m = 2, 5, 10; 11 = (2 mod m) for m = 3, 9; 11 = (3 mod m) for m = 4, 8; 11 = (4 mod m) for m = 7; 11 = (5 mod m) for m = 6, so that (row 4) = (3,2,2,1,1). MATHEMATICA z = 60; f[n_, m_, k_] := f[n, m, k] = If[Mod[Prime[n], m] == k, 1, 0]; t[k_] := t[k] = Table[f[n, m, k], {n, 1, z}, {m, 1, -1 + Prime[n]}]; u = Table[Count[t[k][[i]], 1], {k, 1, 40}, {i, 1, z}]; v = Table[u[[n, k]], {k, 2, 20}, {n, 1, (-1 + Prime[k])/2}] Flatten[v] (* A244740 *) CROSSREFS Cf. A000040, A244796, A244797, A244798, A244799, A244800. Sequence in context: A229214 A218578 A006346 * A088742 A256435 A279945 Adjacent sequences:  A244737 A244738 A244739 * A244741 A244742 A244743 KEYWORD nonn,easy,tabf AUTHOR Clark Kimberling, Jul 06 2014 STATUS approved

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Last modified April 20 19:23 EDT 2021. Contains 343137 sequences. (Running on oeis4.)