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

Author

Amiram Eldar, Nov 22 2020

Keywords

• nonn
• base

Comments

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

Examples

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

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.

Crossrefs

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

Programs

Mathematica

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

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