# nice new sequences

N. J. A. Sloane njas at research.att.com
Sat Feb 3 19:38:28 CET 2001

```Gregory Allen (jukebox_999 at hotmail.com) sent in these two seqs:

%I A059458
%S A059458 10,11,111,101,1101,11101,11111,10111,10011,10001,10000000010001,
%T A059458 10000001010001
%N A059458 A binary sequence: a(1) = 10 (2 in decimal), and a(n+1) is obtained by trying to complement just one bit of a(n), starting with the least significant bit, until a new prime is reached.
%C A059458 It is not known if the sequence is infinite.
%O A059458 1,1
%K A059458 nice,nonn,base,more
%A A059458 Gregory Allen (jukebox_999 at hotmail.com), Feb 02 2001
%Y A059458 The decimal sequence is given in A059459. A base ten analogue is in A059471.

%I A059459
%S A059459 2,3,7,5,13,29,31,23,19,17,8209,8273
%N A059459 a(1) = 2; a(n+1) is obtained by writing a(n) in binary and trying to complement just one bit, starting with the least significant bit, until a new prime is reached.
%C A059459 It is not known if the sequence is infinite.
%O A059459 1,1
%K A059459 more,nonn,base,nice
%A A059459 Gregory Allen (jukebox_999 at hotmail.com), Feb 02 2001
%Y A059459 Cf. A059458 (for this sequence written in binary), A059471.

(well, i extended them by hand, so don't blame him for errors)

and I added these two analogues:

%I A059471
%S A059471 2,3,5,7,17,11,13,19,29,23,43,41,47,37,31,61,67,97,197,191
%N A059471 a(1) = 2; a(n+1) is obtained by and trying to change just one digit of a(n), starting with the least significant digit, until a new prime is reached.
%C A059471 It is not known if the sequence is infinite.
%O A059471 1,1
%K A059471 more,nonn,base,nice
%A A059471 njas, Feb 3, 2001
%Y A059471 Decimal analogue of  A059458. See also A059472 for primes that are missed.

%I A059472
%S A059472 53,59,71,73,79,83,89
%N A059472 Primes omitted from A059471.
%O A059472 1,1
%K A059472 more,nonn,base
%A A059472 njas, Feb 3, 2001

The tail end of the database (currently
www.research.att.com/~njas/sequences/eisBTfry00059.html )
also contains a number of other very nice new sequences sent in
by variuos correspondents.

njas

```