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

1,1

Links

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

Formula

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

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 *)

Crossrefs

Cf. A000217, A034963, A226153.

Sequence in context: A119138 A043192 A043972 * A179741 A144312 A062025

Adjacent sequences: A226193 A226194 A226195 * A226197 A226198 A226199

Keyword

nonn

Author

Alex Ratushnyak, May 30 2013

Status

approved