A339081 Initial prime in the least binary Ormiston n-tuple: n consecutive primes whose binary representations are anagrams of each other.

2, 11, 103, 167, 941, 6287, 6287, 150287, 866087, 4813583, 53376151, 80522263, 564779279, 1300664983, 1786616407, 1971072527, 4149916763, 133076127097, 515655598279, 4572291787807, 4572291787807, 4572291787807, 9039081952627, 189984035976239

Offset

1,1

Comments

Equivalently, a(n) is the start of the least run of n consecutive primes with the same length of binary representation (A070939) and the same binary weight (A000120).

Links

Table of n, a(n) for n=1..24.

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

a(1) = 2 since 2 is the least prime number and its binary representation, 10, is not an anagram of the binary representation of the next prime, 3, whose binary representation is 11.
a(2) = 11 since 11 and 13 are the least pair of consecutive primes whose binary representations, 1011 and 1101, are anagrams of each other.
a(3) = 103 since 103, 107 and 109 are the least triple of consecutive primes whose binary representations, 1100111, 1101011 and 1101101, are anagrams of each other.

Mathematica

s[n_] := Sort[IntegerDigits[n, 2]]; orm[mx_] := Module[{p1 = p2 = 2, c = 1, m = 0, seq, s1, s2}, s1 = s[p1]; seq = Table[0, {mx}]; seq[[1]] = p1; While[c < mx, p2 = NextPrime[p2]; If[(s2 = s[p2]) == s1, c++; If[seq[[c]] == 0, seq[[c]] = p1], c = 1; p1 = p2; s1 = s2]]; seq]; orm[10]

Crossrefs

Cf. A217372 (decimal analog), A339080.

Sequence in context: A024721 A367852 A285199 * A081716 A334240 A377595

Adjacent sequences: A339078 A339079 A339080 * A339082 A339083 A339084

Keyword

nonn,base,more

Author

Amiram Eldar, Nov 22 2020

Extensions

a(20)-a(24) from Martin Ehrenstein using Kim Walisch's primesieve, Jan 31 2021

Status

approved