Paul V. McKinney - cp's OEIS frontend

User: Paul V. McKinney

Paul V. McKinney has authored 2 sequences.

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

Paul V. McKinney, Jan 07 2022

The intersection of this sequence and A320102 is empty.
A320102|  1|  2|  4|  8| 16| 32| 64|128|256|
--------------------------------------------
    |  3| * |   |   |   |   |   |   |   |
    | * |  7| * | 13|   | 37|   |   |   |
   | * | 19|   |   | * |   |   |   |   |
   | * | 43|   | * |   | * |   |   |   |
   | * |   |   | * | 89|   | * |   |   |
   | * |   |101|   |113| * | * |   |353|
  | * | * | * | * | * | * | * |   |383|
  | * |139|   | * |   |   |   | * |   |
  | * |151| * |157| * |181|   | * |   |
  | * |   | * | * |   | * |   | * |   |
  | * | * | * | * | * | * |   | * |   |
  | * |   |197|   |   |   | * | * |449|
  | * | * | * | * | * |   | * | * |479|
  | * |   |   | * |   | * | * | * |   |
  | * | * | * | * |   | * | * | * |   |
  | * | * |   | * | * | * | * | * |   |
  | * |   |   |   |   |   |   |   | * |
  | * |   | * |   | * |   |   |   | * |
  | * |283|   | * | * |313|   |409| * |
  | * | * |311|   | * | * |   |   | * |
  | * | * |   | * |347|   | * |   | * |
  | * |   |   |   | * |   | * |   | * |
  | * |   | * | * | * |   | * |   | * |
  | * |   | * |   | * | * | * |   | * |
  | * |   | * |397|   |421|   | * | * |
  | * |   |   |409| * |433|   | * | * |
  | * | * | * | * |   | * |   | * | * |
  | * | * |   | * | * | * |   | * | * |
  | * | * |   | * |   | * | * | * | * |
  | * |   | * | * | * | * | * | * | * |

Cf. A320102.

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

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

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

Original entry on oeis.org

2, 5, 17, 41, 73, 97, 127, 137, 149, 173, 191, 193, 223, 233, 239, 251, 257, 277, 281, 307, 331, 337, 349, 373, 389, 401, 431, 443, 491, 509, 521, 547, 557, 569, 577, 599, 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

Offset: 1

Paul V. McKinney, Oct 06 2018

Rooms in Paulsen's prime number maze that are not connected to any room with a lesser room number.
"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).
If k is prime and the bit 2^m in k is 0 then 2^m+k is not in the sequence.
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

			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}.
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}.

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Paul V. McKinney, Fortran Program.

Cf. A019434, A137985, A065092, A065111, A065123.

FORTRAN
```
See "Links" for program.
```

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 *)

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

from sympy import isprime
def ok(n):
    if not isprime(n): return False
    onelocs = (i for i, bi in enumerate(bin(n)[2:][::-1]) if bi == '1')
    return not any(isprime(n-2**k) for k in onelocs)
print([k for k in range(1154) if ok(k)]) # Michael S. Branicky, Jan 10 2022

cp's OEIS Frontend

User: Paul V. McKinney

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Python

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

FORTRAN

Mathematica

PARI

Python