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
Examples
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.
Links
- 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.
Programs
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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]
Extensions
a(20)-a(24) from Martin Ehrenstein using Kim Walisch's primesieve, Jan 31 2021
Comments