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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)?

LINKS

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

EXAMPLE

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;

PROG

(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);

CROSSREFS

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

Cf. A152451.

Sequence in context: A003629 A175865 A001122 * A329760 A156221 A207325

Adjacent sequences:  A152868 A152869 A152870 * A152872 A152873 A152874

KEYWORD

nonn,easy,tabf

AUTHOR

Vladimir Shevelev, Dec 14 2008

EXTENSIONS

Heavily edited by Jason Kimberley, Feb 12 2013

STATUS

approved

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Last modified April 15 02:27 EDT 2021. Contains 342974 sequences. (Running on oeis4.)