A082740 Square root of the sum of the terms of the n-th row of A082737.

1, 3, 5, 12, 19, 20, 25, 42, 39, 46, 73, 74, 79, 86, 95, 104, 141, 136, 143, 170, 171, 192, 197, 220, 225, 244, 255, 272, 303, 310, 325, 340, 357, 390, 399, 418, 455, 462, 473, 494, 549, 546, 579, 580, 599, 678, 651, 668, 705, 732, 737, 758, 825, 832, 833, 864

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Maple

A082740 := proc(nmax) local T, a, n, r, i, rsum, c, j ; T := [1, 2, 7] ; a := [1, 3] ; n := 3 ; i := 1 ; while nops(a)< nmax do r := [] ; for c from 1 to n-1 do while ithprime(i) in T or ithprime(i) in r do i:= i+1 ; od ; r := [op(r), ithprime(i)] ; i:= i+1 ; od ; j := i+1 ; rsum := sum(op(k, r), k=1..nops(r)) ; while not issqr( rsum+ithprime(j)) do j := j+1 ; od ; r := [op(r), ithprime(j)] ; a := [op(a), sqrt(sum(op(l, r), l=1..nops(r)))] ; T := [op(T), op(r)] ; n := n+1 ; od ; RETURN(a) ; end: a := A082740(80) : for n from 1 to nops(a) do printf("%d, ", op(n, a)) ; od ; # R. J. Mathar, Nov 12 2006

Mathematica

A082737[nmax_] := Module[{a, n, r, i, rsum, c, j}, a = {1, 2, 7}; n = 3; i = 1; While[Length[a] <= nmax, r = {}; For[c = 1, c <= n - 1, c++, While[MemberQ[a, Prime[i]] || MemberQ[r, Prime[i]], i++]; r = Append[r, Prime[i]]; i++]; j = i + 1; rsum = Total[r]; While[! IntegerQ@Sqrt[rsum + Prime[j]], j++]; r = Append[r, Prime[j]]; a = Join[a, r]; n++]; Return[a]];
rows = 56;
nmax = rows (rows + 1)/2;
tri = A082737[nmax];
T = Table[tri[[(n^2 - n + 2)/2 ;; n (n + 1)/2]], {n, 1, rows}];
a[n_] := Sqrt@Sum[T[[n, k]], {k, 1, n}];
Table[a[n], {n, 1, rows}] (* Jean-François Alcover, Apr 04 2024, after R. J. Mathar *)

Crossrefs

Cf. A082737, A082738, A082739.

Sequence in context: A279784 A198301 A323866 * A010067 A341710 A024458

Adjacent sequences: A082737 A082738 A082739 * A082741 A082742 A082743

Keyword

nonn

Author

Amarnath Murthy, Apr 14 2003

Extensions

More terms from R. J. Mathar, Nov 12 2006

Status

approved