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%I #11 Apr 04 2024 07:53:37
%S 1,3,5,12,19,20,25,42,39,46,73,74,79,86,95,104,141,136,143,170,171,
%T 192,197,220,225,244,255,272,303,310,325,340,357,390,399,418,455,462,
%U 473,494,549,546,579,580,599,678,651,668,705,732,737,758,825,832,833,864
%N Square root of the sum of the terms of the n-th row of A082737.
%p 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
%t 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]];
%t rows = 56;
%t nmax = rows (rows + 1)/2;
%t tri = A082737[nmax];
%t T = Table[tri[[(n^2 - n + 2)/2 ;; n (n + 1)/2]], {n, 1, rows}];
%t a[n_] := Sqrt@Sum[T[[n, k]], {k, 1, n}];
%t Table[a[n], {n, 1, rows}] (* _Jean-François Alcover_, Apr 04 2024, after _R. J. Mathar_ *)
%Y Cf. A082737, A082738, A082739.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Apr 14 2003
%E More terms from _R. J. Mathar_, Nov 12 2006
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