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 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. 8
 2, 3, 7, 5, 13, 29, 31, 23, 19, 17, 8209, 8273, 10321, 2129, 2131, 83, 67, 71, 79, 1103, 1039, 1031, 1063, 1061, 1069, 263213, 263209, 263201, 265249, 265313, 264289, 280673, 280681, 280697, 280699, 280703, 280639, 280607, 280603, 280859, 280843, 281867, 265483, 265547, 265579, 265571, 266083, 266081, 266089, 266093, 266029 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is the lexicographically least (in positions of the flipped bits) such sequence. It is not known if the sequence is infinite. "The prime maze - consider the prime numbers in base 2, starting with the smallest prime (10)2. One can move to another prime number by either changing only one digit of the number, or adding a 1 to the front of the number. Can we reach 11 = (1011)2.? 3331? The Mersennes?" (See 'Prime Links + +'.) If we start at 11 and exclude terms 2 and 3 we get terms 11, 43, 41, and so on. This is the opposite parity sequence. a(130), if it exists, is greater than 2^130000. - Charles R Greathouse IV, Jan 02 2014 a(130) is equal to a(129) + 2^400092. - Giovanni Resta, Jul 19 2017 LINKS T. D. Noe and Charles R Greathouse IV, Table of n, a(n) for n = 1..129 (first 104 terms from Noe) Chris K. Caldwell, Prime Links + + W. Paulsen, The Prime Number Maze, Web Pages. W. Paulsen, The Prime Number Maze, Fib. Quart., 40 (2002), 272-279. Carlos Rivera, Problem 25.- William Paulsen's Prime Numbers Maze MAPLE A059459search := proc(a, upto_bit, upto_length) local i, n, t; if(nops(a) >= upto_length) then RETURN(a); fi; t := a[nops(a)]; for i from 0 to upto_bit do n := XORnos(t, (2^i)); if(isprime(n) and (not member(n, a))) then print([op(a), n]); RETURN(A059459search([op(a), n], upto_bit, upto_length)); fi; od; RETURN([op(a), `and no more`]); end; E.g., call as: A059459search(, 128, 200); MATHEMATICA maxBits = 2^11; ClearAll[a]; a = 2; 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, 129}] (* Jean-François Alcover, Jan 17 2012 *) f[lst_List] := Block[{db2 = IntegerDigits[lst[[-1]], 2]}, exp = Length@ db2; While[pp = db2; pp[[exp]] = If[OddQ@db2[[exp]], 0, 1]; pp = FromDigits[pp, 2]; !PrimeQ[pp] || MemberQ[lst, pp], exp--; If[exp == 0, exp++; PrependTo[db2, 0]]]; Append[lst, pp]]; Nest[f, {2}, 128] (* Robert G. Wilson v, Jul 17 2017 *) PROG (PARI) step(n)=my(k, t); while(vecsearch(v, t=bitxor(n, 1<

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Last modified March 23 22:07 EDT 2019. Contains 321443 sequences. (Running on oeis4.)