A339080 Smaller members of binary Ormiston prime pairs: two consecutive primes whose binary representations are anagrams of each other.

11, 23, 37, 59, 83, 103, 107, 131, 139, 151, 167, 173, 179, 199, 227, 229, 263, 277, 347, 409, 419, 439, 487, 491, 503, 557, 563, 613, 647, 653, 659, 683, 719, 727, 757, 811, 823, 827, 839, 853, 911, 941, 947, 953, 967, 997, 1019, 1063, 1091, 1093, 1123, 1163

Offset

1,1

Comments

Equivalently, the smaller of two consecutive primes with the same length of binary representation (A070939) and the same binary weight (A000120).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Jens Kruse Andersen, Ormiston Tuples.

Andy Edwards, Ormiston Pairs, Australian Mathematics Teacher, Vol. 58, No. 2 (2002), pp. 12-13.

Giovanni Resta, Ormiston pairs.

Eric Weisstein's World of Mathematics, Rearrangement Prime Pair.

Example

11 is a term since 11 and 13 are consecutive primes whose binary representations, 1011 and 1101, are anagrams of each other.

Mathematica

Transpose[Select[Partition[Prime[Range[200]], 2, 1], Sort[IntegerDigits[First[#], 2]] == Sort[IntegerDigits[Last[#], 2]]&]][[1]] (* after Harvey P. Dale at A069567 *)

Prog

(Python)
from sympy import nextprime
from itertools import islice
def hash(n): return "".join(sorted(bin(n)[2:]))
def agen(start=2): # generator of terms
    p = nextprime(start-1); q=nextprime(p)
    hp, hq = list(map(hash, [p, q]))
    while True:
        if hp == hq: yield p
        p, q = q, nextprime(q)
        hp, hq = hq, hash(q)
print(list(islice(agen(), 52))) # Michael S. Branicky, Feb 19 2024

Crossrefs

Cf. A000120, A069567 (decimal analog), A070939, A072274.

Sequence in context: A139493 A275591 A250665 * A077345 A130282 A019356

Adjacent sequences: A339077 A339078 A339079 * A339081 A339082 A339083

Keyword

nonn,base

Author

Amiram Eldar, Nov 22 2020

Status

approved