A262365 A(n,k) is the n-th prime whose binary expansion begins with the binary expansion of k; square array A(n,k), n>=1, k>=1, read by antidiagonals.

2, 2, 3, 3, 5, 5, 17, 7, 11, 7, 5, 19, 13, 17, 11, 13, 11, 37, 29, 19, 13, 7, 53, 23, 67, 31, 23, 17, 17, 29, 97, 41, 71, 53, 37, 19, 19, 67, 31, 101, 43, 73, 59, 41, 23, 41, 37, 71, 59, 103, 47, 79, 61, 43, 29, 11, 43, 73, 131, 61, 107, 83, 131, 97, 47, 31

Offset

1,1

Links

Alois P. Heinz, Antidiagonals n = 1..200, flattened

Index entries for primes involving decimal expansion of n

Example

Square array A(n,k) begins:
:  2,  2,  3,  17,  5,  13,   7,  17, ...
:  3,  5,  7,  19, 11,  53,  29,  67, ...
:  5, 11, 13,  37, 23,  97,  31,  71, ...
:  7, 17, 29,  67, 41, 101,  59, 131, ...
: 11, 19, 31,  71, 43, 103,  61, 137, ...
: 13, 23, 53,  73, 47, 107, 113, 139, ...
: 17, 37, 59,  79, 83, 109, 127, 257, ...
: 19, 41, 61, 131, 89, 193, 227, 263, ...

Maple

u:= (h, t)-> select(isprime, [seq(h*2^t+k, k=0..2^t-1)]):
A:= proc(n, k) local l, p;
      l:= proc() [] end; p:= proc() -1 end;
      while nops(l(k))<n do p(k):= p(k)+1;
        l(k):= [l(k)[], u(k, p(k))[]]
      od: l(k)[n]
    end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..14);

Mathematica

nmax = 14;
col[k_] := col[k] = Module[{bk = IntegerDigits[k, 2], lk, pp = {}, coe = 1}, lbk = Length[bk]; While[Length[pp] < nmax, pp = Select[Prime[Range[ coe*nmax]], Quiet@Take[IntegerDigits[#, 2], lbk] == bk&]; coe++]; pp];
A[n_, k_] := col[k][[n]];
Table[A[n-k+1, k], {n, 1, nmax}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Oct 25 2021 *)

Crossrefs

Columns k=1-7 give: A000040, A080165, A080166, A262286, A262284, A262287, A262285.

Row n=1 gives A164022.

Main diagonal gives A262366.

Cf. A262350, A262369.

Sequence in context: A342654 A166588 A277321 * A063988 A198453 A345162

Adjacent sequences: A262362 A262363 A262364 * A262366 A262367 A262368

Keyword

nonn,look,base,tabl

Author

Alois P. Heinz, Sep 20 2015

Status

approved