A226196 Triangular numbers which are an average of four consecutive primes.

15, 55, 105, 120, 253, 595, 1225, 1485, 2080, 2211, 3321, 4371, 5460, 6786, 7381, 7503, 10731, 11935, 12246, 16290, 18915, 24531, 24753, 27966, 36585, 44850, 51360, 55278, 55945, 56953, 60031, 64980, 68265, 69006, 70125, 75078, 86736, 87153, 92235, 94830, 98790, 111628

Offset: 1

Author

Alex Ratushnyak, May 30 2013

Keywords

• nonn

Links

• Zak Seidov, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A000217, A034963, A226153.

Programs

Maple

A000217inv:=proc(n)
    local t1;
    t1:=floor(sqrt(2*n));
    if n = t1*(t1+1)/2 then
        return t1 ;
    else
        return -1;
    end if;
end proc:
for n from 1 to 90000 do
    s := A034963(n)/4 ;
    if type(s, 'integer') then
        tr := A000217inv(s) ;
        if tr >= 0  then
            printf("%d, ", s) ;
        end if;
    end if;
end do: # R. J. Mathar, Jun 06 2013

Mathematica

Select[Mean/@Partition[Prime[Range[20000]],4,1],OddQ[Sqrt[8#+1]]&] (* Harvey P. Dale, Dec 18 2015 *)

Formula

a(n) = A000217(A226153(n)).