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A320102 Primes where changing any single bit in the binary representation never results in a smaller prime.

%I A320102 #47 Jan 13 2022 04:22:02
%S A320102 2,5,17,41,73,97,127,137,149,173,191,193,223,233,239,251,257,277,281,
%T A320102 307,331,337,349,373,389,401,431,443,491,509,521,547,557,569,577,599,
%U A320102 617,641,653,683,701,719,733,757,761,787,809,821,839,853,877,881,907,919,977,997,1019,1033,1087,1093,1153
%N A320102 Primes where changing any single bit in the binary representation never results in a smaller prime.
%C A320102 Rooms in Paulsen's prime number maze that are not connected to any room with a lesser room number.
%C A320102 "The prime number maze is a maze of prime numbers where two primes are connected if and only if their base 2 representations differ in just one bit." - William Paulsen (A065123).
%C A320102 If k is prime and the bit 2^m in k is 0 then 2^m+k is not in the sequence.
%C A320102 If k is in the sequence then 2^m+k is not where the bit 2^m in k is 0. - _David A. Corneth_, Oct 09 2018
%H A320102 Michael S. Branicky, <a href="/A320102/b320102.txt">Table of n, a(n) for n = 1..10000</a>
%H A320102 Paul V. McKinney, <a href="/A320102/a320102.txt">Fortran Program</a>.
%e A320102 7 is not in the sequence because there is a way to change only one single bit of its binary representation that results in a prime smaller than 7 {1(1)1,(1)11} {5,3}.
%e A320102 41 is in the sequence because changing any single bit of its binary representation binary representation never results in a smaller prime {10100(1),10(1)001,(1)01001} {40,25,9}.
%t A320102 q[p_] := PrimeQ[p] && AllTrue[2^(-1 + Position[Reverse @ IntegerDigits[p, 2], 1] // Flatten), !PrimeQ[p - #] &]; Select[Range[1000], q] (* _Amiram Eldar_, Jan 13 2022 *)
%o A320102 (PARI) is(n) = if(!isprime(n), return(0)); b = binary(n); for(i=1, #b, if(b[i]==1, if(isprime(n-2^(#b-i)), return(0)))); 1 \\ _David A. Corneth_, Oct 09 2018
%o A320102 (FORTRAN) See "Links" for program.
%o A320102 (Python)
%o A320102 from sympy import isprime
%o A320102 def ok(n):
%o A320102     if not isprime(n): return False
%o A320102     onelocs = (i for i, bi in enumerate(bin(n)[2:][::-1]) if bi == '1')
%o A320102     return not any(isprime(n-2**k) for k in onelocs)
%o A320102 print([k for k in range(1154) if ok(k)]) # _Michael S. Branicky_, Jan 10 2022
%Y A320102 Cf. A019434, A137985, A065092, A065111, A065123.
%K A320102 base,nonn
%O A320102 1,1
%A A320102 _Paul V. McKinney_, Oct 06 2018