cp's OEIS Frontend

A024320 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (1, p(1), p(2), ... ).

%I A024320 #13 Jan 28 2022 22:57:12
%S A024320 0,0,2,3,5,7,11,13,24,30,36,46,50,60,70,74,103,117,131,139,157,171,
%T A024320 177,193,207,221,278,294,310,330,348,360,390,408,424,448,470,486,573,
%U A024320 611,625,653,673,699,739,761,781,803,835,863,891,925,1054,1078,1104,1136,1180,1214
%N A024320 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (1, p(1), p(2), ... ).
%H A024320 G. C. Greubel, <a href="/A024320/b024320.txt">Table of n, a(n) for n = 1..1000</a>
%F A024320 a(n) = A023531(1) + Sum_{j=2..floor((n+1)/2)} A023531(j)*Prime(n-j+1). - _G. C. Greubel_, Jan 19 2022
%t A024320 A023531[n_]:= SquaresR[1, 8*n+9]/2;
%t A024320 p[n_]:= If[n==1, 1, Prime[n-1]];
%t A024320 a[n_]:= Sum[A023531[j]*p[n-j+1], {j, Floor[(n+1)/2]}];
%t A024320 Table[a[n], {n, 60}] (* _G. C. Greubel_, Jan 19 2022 *)
%o A024320 (Magma)
%o A024320 A023531:= func< n | IsIntegral( (Sqrt(8*n+9) -3)/2 ) select 1 else 0 >;
%o A024320 p:= func< n | n eq 1 select 1 else NthPrime(n-1) >;
%o A024320 [ (&+[A023531(j)*p(n-j+1): j in [1..Floor((n+1)/2)]]) : n in [1..60]]; // _G. C. Greubel_, Jan 19 2022
%o A024320 (Sage)
%o A024320 def A023531(n):
%o A024320     if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
%o A024320     else: return 0
%o A024320 def p(n):
%o A024320     if (n==1): return 1
%o A024320     else: return nth_prime(n-1)
%o A024320 [sum( A023531(j)*p(n-j+1) for j in (1..floor((n+1)/2)) ) for n in (1..60)] # _G. C. Greubel_, Jan 19 2022
%Y A024320 Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024321, A024322, A024323, A024324, A024325, A024326, A024327.
%Y A024320 Cf. A000040, A023531.
%K A024320 nonn
%O A024320 1,3
%A A024320 _Clark Kimberling_