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

3, 7, 13, 19, 37, 43, 89, 101, 113, 139, 151, 157, 181, 197, 283, 311, 313, 347, 353, 383, 397, 409, 421, 433, 449, 479, 523, 563, 571, 593, 607, 619, 631, 643, 661, 673, 727, 751, 769, 811, 823, 829, 883, 911, 937, 967, 971, 983, 1009, 1013, 1021, 1049, 1097

Offset

1,1

Comments

The intersection of this sequence and A320102 is empty.

A320102| 1| 2| 4| 8| 16| 32| 64|128|256|

--------------------------------------------

2 | 3| * | | | | | | | |

5 | * | 7| * | 13| | 37| | | |

17 | * | 19| | | * | | | | |

41 | * | 43| | * | | * | | | |

73 | * | | | * | 89| | * | | |

97 | * | |101| |113| * | * | |353|

127 | * | * | * | * | * | * | * | |383|

137 | * |139| | * | | | | * | |

149 | * |151| * |157| * |181| | * | |

173 | * | | * | * | | * | | * | |

191 | * | * | * | * | * | * | | * | |

193 | * | |197| | | | * | * |449|

223 | * | * | * | * | * | | * | * |479|

233 | * | | | * | | * | * | * | |

239 | * | * | * | * | | * | * | * | |

251 | * | * | | * | * | * | * | * | |

257 | * | | | | | | | | * |

277 | * | | * | | * | | | | * |

281 | * |283| | * | * |313| |409| * |

307 | * | * |311| | * | * | | | * |

331 | * | * | | * |347| | * | | * |

337 | * | | | | * | | * | | * |

349 | * | | * | * | * | | * | | * |

373 | * | | * | | * | * | * | | * |

389 | * | | * |397| |421| | * | * |

401 | * | | |409| * |433| | * | * |

431 | * | * | * | * | | * | | * | * |

443 | * | * | | * | * | * | | * | * |

491 | * | * | | * | | * | * | * | * |

509 | * | | * | * | * | * | * | * | * |

Links

Table of n, a(n) for n=1..53.

Prog

(Python)
from sympy import isprime, primerange
def ok320102(p):
    onelocs = (i for i, bi in enumerate(bin(p)[2:][::-1]) if bi == '1')
    return not any(isprime(p-2**k) for k in onelocs)
def aupto(limit):
    alst = []
    A350591 = set(p for p in primerange(1, limit+1) if ok320102(p))
    for p in primerange(1, limit+1):
        onelocs = (i for i, bi in enumerate(bin(p)[2:][::-1]) if bi == '1')
        if any(p-2**k in A350591 for k in onelocs):
            alst.append(p)
    return alst
print(aupto(770)) # Michael S. Branicky, Jan 10 2022

Crossrefs

Cf. A320102.

Sequence in context: A023200 A046136 A098044 * A252091 A217035 A134765

Adjacent sequences: A350588 A350589 A350590 * A350592 A350593 A350594

Keyword

base,nonn

Author

Paul V. McKinney, Jan 07 2022

Extensions

a(27) and beyond from Michael S. Branicky, Jan 10 2022

Status

approved