A152871 Irregular table with first row containing the single term 3; in the n-th row, n>=2, we list in increasing order those d=2^(n+1)-a, for each term a in all the preceding rows, such that d is prime.

3, 5, 11, 13, 19, 29, 53, 59, 61, 67, 109, 197, 227, 251, 499, 509, 773, 797, 827, 971, 1013, 1019, 1021, 1549, 1987, 2029, 3083, 3299, 3323, 4091, 4093, 4099, 6163, 8179, 15413, 16187, 16381, 28669, 30781, 31219, 32707, 32749, 50123, 62213, 64709, 64763

Offset: 1

Author

Vladimir Shevelev, Dec 14 2008

Keywords

• nonn
• easy
• tabf

Comments

Since primes above the n-th row are <2^n, primes in the n-th row are >2^(n+1)-2^n=2^n. Thus in different rows primes are different.

Questions: 1) Is every row nonempty? 2) Is the sequence infinite (an infinite number of nonempty rows)?

Examples

			1: 3;
2: 5;
3: 11, 13;
4: 19, 29;
5: 53, 59, 61;
6: 67, 109;
7: 197, 227, 251;
8: 499, 509;
9: 773, 797, 827, 971, 1013, 1019, 1021;
		

Links

• Jason Kimberley, Table of n, a(n) for n = 1..1016

Crossrefs

The n-th row has length A152872(n).

Cf. A152451.

Programs

Magma

A152871and2 :=
    function(N)
        A := [[3]]; C := [1];
        for n in [2..N] do
            C[n] := 0;
            A[n] := [];
            for a in Reverse(&cat A) do
                d := 2^(n+1) - a;
                if
                    IsPrime(d)
                then
                    Append(~A[n],d);
                    C[n] +:= 1;
                end if;
            end for;
        end for;
        return A, C;
    end function;
A152871and2(20);

Extensions

Heavily edited by Jason Kimberley, Feb 12 2013