login
A350591
Primes with Hamming distance of one from those in A320102.
1
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 | * | | * | * | * | * | * | * | * |
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
KEYWORD
base,nonn
AUTHOR
Paul V. McKinney, Jan 07 2022
EXTENSIONS
a(27) and beyond from Michael S. Branicky, Jan 10 2022
STATUS
approved