A362979 - OEIS

%I #34 Jan 19 2024 08:13:57

%S 7,11,23,13,29,31,19,43,47,311

%N Square array, read by descending antidiagonals: row n lists the primes whose base-2 representation has exactly n ones, starting from n=3.

%e Corner:

%e   n=3:    7    11    13    19    37   41     67    73    97

%e   n=4:   23    29    43    53    71   83     89   101   113

%e   n=5:   31    47    59    61    79   103   107   109   151

%e   n=6:  311   317   347   349   359   373   461   467   571

%e The first four primes in row n=3 have these base-2 representations, respectively: 111, 1011, 1101, 10011.

%t t[n_] := Count[IntegerDigits[Prime[n], 2], 1]  (* A014499 *)

%t u = Table[t[n], {n, 1, 200}];

%t p[n_] := Flatten[Position[u, n]]

%t w = TableForm[Table[Prime[p[n]], {n, 3, 16}]]

%Y Cf. A000040, A014499.

%Y Cf. A019434 (row 2), A061712 (column 1), A081091 (row 3), A095077 (row 4).

%K nonn,base,tabl,more

%O 3,1

%A _Clark Kimberling_, May 11 2023

%E New offset and edited by _Michel Marcus_, Jan 19 2024