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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.
11
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
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.
Sequence in context: A342654 A166588 A277321 * A063988 A198453 A345162
KEYWORD
nonn,look,base,tabl
AUTHOR
Alois P. Heinz, Sep 20 2015
STATUS
approved