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%I #11 Apr 04 2024 07:54:16
%S 1,2,3,11,23,41,61,89,131,179,233,307,379,449,541,619,727,839,971,
%T 1097,1237,1423,1553,1709,1901,2089,2293,2477,2713,2953,3229,3491,
%U 3719,4001,4271,4583,4909,5209,5521,5851,6211,6563,6949,7331,7717,8147,8573,8969
%N First column of triangle A082737.
%p A082739 := proc(nmax) local T,a,n,r,i,rsum,c,j ; T := [1,2,7] ; a := [1,2] ; 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 ; a := [op(a),op(1,r)] ; r := [op(r),ithprime(j)] ; T := [op(T),op(r)] ; n := n+1 ; od ; RETURN(a) ; end: a := A082739(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 = 48;
%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_] := T[[n, 1]];
%t Table[a[n], {n, 1, rows}] (* _Jean-François Alcover_, Apr 04 2024, after _R. J. Mathar_ *)
%Y Cf. A082737, A082738, A082740.
%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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