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.
Original entry on oeis.org
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
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, ...
-
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))
-
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 *)
A077345
a(n) is the n-th prime whose decimal expansion begins with the decimal expansion of n.
Original entry on oeis.org
11, 23, 37, 401, 509, 617, 719, 829, 953, 1033, 1171, 1279, 1373, 1483, 15013, 1697, 17021, 18049, 19001, 20051, 21067, 22031, 23027, 24097, 25127, 26107, 27103, 28123, 29153, 30161, 31159, 32189, 33161, 34259, 35171, 36241, 37243, 38299, 39241, 40237, 41263
Offset: 1
-
u:= (h, t)-> select(isprime, [seq(h*10^t+k, k=0..10^t-1)]):
A:= proc(n, k) local l, p;
l:= proc() [] end; p:= proc() -1 end;
while nops(l(k)) A(n$2):
seq(a(n), n=1..45); # Alois P. Heinz, Sep 30 2015
-
u[h_, t_] := Select[Table[h*10^t + k, {k, 0, 10^t - 1}], PrimeQ];
A[n_, k_] := Module[{l, p}, l[] = {}; p[] = -1; While[Length[l[k]] < n, p[k] = p[k] + 1; l[k] = Join[l[k], u[k, p[k]]]]; l[k][[n]]];
a[n_] := A[n, n];
Table[a[n], {n, 1, 45}] (* Jean-François Alcover, Oct 25 2021, after Alois P. Heinz *)
A077344
Triangle in which n-th row contains n smallest primes beginning with n.
Original entry on oeis.org
11, 2, 23, 3, 31, 37, 41, 43, 47, 401, 5, 53, 59, 503, 509, 61, 67, 601, 607, 613, 617, 7, 71, 73, 79, 701, 709, 719, 83, 89, 809, 811, 821, 823, 827, 829, 97, 907, 911, 919, 929, 937, 941, 947, 953, 101, 103, 107, 109, 1009, 1013, 1019, 1021, 1031, 1033
Offset: 1
Triangle begins:
: 11;
: 2, 23;
: 3, 31, 37;
: 41, 43, 47, 401;
: 5, 53, 59, 503, 509;
: 61, 67, 601, 607, 613, 617;
: 7, 71, 73, 79, 701, 709, 719;
: 83, 89, 809, 811, 821, 823, 827, 829;
: 97, 907, 911, 919, 929, 937, 941, 947, 953;
: 101, 103, 107, 109, 1009, 1013, 1019, 1021, 1031, 1033;
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