A388071 Numbers that are both the sum of three consecutive primes and the sum of three consecutive squares.

4565, 17789, 19685, 29405, 33077, 42485, 43925, 45389, 68405, 87725, 109445, 186005, 189005, 204365, 268205, 348845, 412925, 501845, 637565, 699869, 878045, 950909, 1279229, 1366877, 1737365, 1811189, 2152229, 2457077, 2816885, 3054245, 3066365, 3878309, 4198469, 4531325, 4665029, 5298725

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 19685 is a term because 19685 = 6553 + 6563 + 6569 (three consecutive primes) and 19685 = 80^2 + 81^2 + 82^2 (three consecutive squares).

Maple

iss3p:= proc(z)
  local p, q, r;
    p:= prevprime((z+1)/3);
    q:= nextprime(p);
    if 2*p+q > z then r:= prevprime(p)
    else r:= nextprime(q)
    fi;
    p+q+r = z
end proc:
select(iss3p, [seq(3*x^2+2, x=3..2000, 2)]); # Robert Israel, Feb 26 2026

Crossrefs

Intersection of A034961 and A120328.

Sequence in context: A102748 A032751 A020436 * A104947 A030471 A234677

Adjacent sequences: A388068 A388069 A388070 * A388072 A388073 A388074

Keyword

nonn

Author

Robert Israel, Dec 11 2025

Status

approved