A359664 Prime Maze Room 11, opposite parity of A059459 starting from prime room 11.

11, 43, 41, 2089, 2081, 2083, 2087, 10889035741470030830827987437816582768679, 10889035741470030830827987437816582768647

Offset

1,1

Comments

This is the opposite parity sequence of A059459 and lexicographically least of this sequence.

It is currently not known whether both of these sequences are infinite.

I was able to calculate 40 terms; a(40) is a 3261-digit prime.

a(1) = 11; 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. (Terms 2 and 3 are excluded values from the main sequence.)

Conjecture: Room 2 and Room 11 are unlinked, i.e., two separate mazes or branches/trees, as they are of opposite parities.

Links

Table of n, a(n) for n=1..9.

Gregory Allen, Table of n, a(n) for n = 1..40

William Paulsen, Prime Maze, See Prime room 11.

Carlos Rivera, Problem 25. William Paulsen's Prime Numbers Maze, The Prime Puzzles and Problems Connection.

Mathematica

maxBits = 2^14;
ClearAll[a];
a[1] = 3;
a[2] = 2;
a[3] = 11;
n = 4;
a[n_] :=
 a[n] = If[PrimeQ[a[n - 1]],
   bits = PadLeft[IntegerDigits[a[n - 1], 2], maxBits];
   For[i = 1, i <= maxBits, i++, bits2 = bits;
    bits2[[-i]] = 1 - bits[[-i]];
    If[i == maxBits, Print["maxBits reached"]; Break[],
     If[PrimeQ[an = FromDigits[bits2, 2]] &&
       FreeQ[Table[a[k], {k, 1, n - 1}], an], Return[an]]]],
   0]; Table[a[n], {n, 42}]

Crossrefs

Cf. A059459.

Sequence in context: A228811 A096638 A089712 * A155711 A226617 A222184

Adjacent sequences: A359661 A359662 A359663 * A359665 A359666 A359667

Keyword

nonn,less

Author

Gregory Allen, Jan 10 2023

Status

approved