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A350591 Primes with Hamming distance of one from those in A320102.

%I A350591 #18 Feb 18 2022 23:00:29
%S A350591 3,7,13,19,37,43,89,101,113,139,151,157,181,197,283,311,313,347,353,
%T A350591 383,397,409,421,433,449,479,523,563,571,593,607,619,631,643,661,673,
%U A350591 727,751,769,811,823,829,883,911,937,967,971,983,1009,1013,1021,1049,1097
%N A350591 Primes with Hamming distance of one from those in A320102.
%C A350591 The intersection of this sequence and A320102 is empty.
%C A350591 A320102|  1|  2|  4|  8| 16| 32| 64|128|256|
%C A350591 --------------------------------------------
%C A350591 2      |  3| * |   |   |   |   |   |   |   |
%C A350591 5      | * |  7| * | 13|   | 37|   |   |   |
%C A350591 17     | * | 19|   |   | * |   |   |   |   |
%C A350591 41     | * | 43|   | * |   | * |   |   |   |
%C A350591 73     | * |   |   | * | 89|   | * |   |   |
%C A350591 97     | * |   |101|   |113| * | * |   |353|
%C A350591 127    | * | * | * | * | * | * | * |   |383|
%C A350591 137    | * |139|   | * |   |   |   | * |   |
%C A350591 149    | * |151| * |157| * |181|   | * |   |
%C A350591 173    | * |   | * | * |   | * |   | * |   |
%C A350591 191    | * | * | * | * | * | * |   | * |   |
%C A350591 193    | * |   |197|   |   |   | * | * |449|
%C A350591 223    | * | * | * | * | * |   | * | * |479|
%C A350591 233    | * |   |   | * |   | * | * | * |   |
%C A350591 239    | * | * | * | * |   | * | * | * |   |
%C A350591 251    | * | * |   | * | * | * | * | * |   |
%C A350591 257    | * |   |   |   |   |   |   |   | * |
%C A350591 277    | * |   | * |   | * |   |   |   | * |
%C A350591 281    | * |283|   | * | * |313|   |409| * |
%C A350591 307    | * | * |311|   | * | * |   |   | * |
%C A350591 331    | * | * |   | * |347|   | * |   | * |
%C A350591 337    | * |   |   |   | * |   | * |   | * |
%C A350591 349    | * |   | * | * | * |   | * |   | * |
%C A350591 373    | * |   | * |   | * | * | * |   | * |
%C A350591 389    | * |   | * |397|   |421|   | * | * |
%C A350591 401    | * |   |   |409| * |433|   | * | * |
%C A350591 431    | * | * | * | * |   | * |   | * | * |
%C A350591 443    | * | * |   | * | * | * |   | * | * |
%C A350591 491    | * | * |   | * |   | * | * | * | * |
%C A350591 509    | * |   | * | * | * | * | * | * | * |
%o A350591 (Python)
%o A350591 from sympy import isprime, primerange
%o A350591 def ok320102(p):
%o A350591     onelocs = (i for i, bi in enumerate(bin(p)[2:][::-1]) if bi == '1')
%o A350591     return not any(isprime(p-2**k) for k in onelocs)
%o A350591 def aupto(limit):
%o A350591     alst = []
%o A350591     A350591 = set(p for p in primerange(1, limit+1) if ok320102(p))
%o A350591     for p in primerange(1, limit+1):
%o A350591         onelocs = (i for i, bi in enumerate(bin(p)[2:][::-1]) if bi == '1')
%o A350591         if any(p-2**k in A350591 for k in onelocs):
%o A350591             alst.append(p)
%o A350591     return alst
%o A350591 print(aupto(770)) # _Michael S. Branicky_, Jan 10 2022
%Y A350591 Cf. A320102.
%K A350591 base,nonn
%O A350591 1,1
%A A350591 _Paul V. McKinney_, Jan 07 2022
%E A350591 a(27) and beyond from _Michael S. Branicky_, Jan 10 2022