A082739 First column of triangle A082737.

1, 2, 3, 11, 23, 41, 61, 89, 131, 179, 233, 307, 379, 449, 541, 619, 727, 839, 971, 1097, 1237, 1423, 1553, 1709, 1901, 2089, 2293, 2477, 2713, 2953, 3229, 3491, 3719, 4001, 4271, 4583, 4909, 5209, 5521, 5851, 6211, 6563, 6949, 7331, 7717, 8147, 8573, 8969

Offset

1,2

Links

Table of n, a(n) for n=1..48.

Maple

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

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 = 48;
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_] := T[[n, 1]];
Table[a[n], {n, 1, rows}] (* Jean-François Alcover, Apr 04 2024, after R. J. Mathar *)

Crossrefs

Cf. A082737, A082738, A082740.

Sequence in context: A350853 A080153 A040124 * A158017 A346605 A091310

Adjacent sequences: A082736 A082737 A082738 * A082740 A082741 A082742

Keyword

nonn

Author

Amarnath Murthy, Apr 14 2003

Extensions

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

Status

approved