A075093 Smallest member of Ormiston prime triple.

11117123, 12980783, 14964017, 32638213, 32964341, 33539783, 35868013, 44058013, 46103237, 48015013, 50324237, 52402783, 58005239, 60601237, 61395239, 74699789, 76012879, 78163123, 80905879, 81966341, 82324237

Offset: 1

Author

Robert G. Wilson v, Aug 31 2002

Keywords

• base
• nonn

Comments

A subsequence of A069567 which is in turn a subsequence of A072274. More precisely, this A075093 lists exactly the terms which precede repeated elements in A072274, since an Ormiston triple (p,q,r), i.e., three consecutive primes whose decimal representations are anagrams of each other, corresponds to two pairs (p,q) and (q,r), so that p=a(n) implies p=A072274(2k-1)=A069567(k) for some k, and q=A072274(2k)=A072274(2k+1)=A069567(k+1) and r=A072274(2k+2). - M. F. Hasler, Oct 11 2012

Examples

			The first Ormiston triples are 11117123, 11117213 and 11117321.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A069567 - smaller member of an Ormiston prime pair.

Cf. A072274, A161160, A066540. - M. F. Hasler, Oct 11 2012

Programs

Haskell

a075093 n = a075093_list !! (n-1)
a075093_list = f a000040_list where
   f (p:ps@(q:r:_)) =
     if sort (show p) == sort (show q) && sort (show q) == sort (show r)
        then p : f ps else f ps
-- Reinhard Zumkeller, Mar 09 2012

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = 0; b = 1; Do[c = NextPrim[b]; If[ Sort[ IntegerDigits[a]] == Sort[ IntegerDigits[b]] == Sort[ IntegerDigits[c]], Print[a]]; a = b; b = c, {n, 1, 10^7}]
op3Q[{a_,b_,c_}]:=Sort[IntegerDigits[a]]==Sort[IntegerDigits[b]] == Sort[ IntegerDigits[ c]]; Transpose[Select[Partition[Prime[ Range[ 5000000]],3,1], op3Q]][[1]] (* Harvey P. Dale, Jun 16 2014 *)

PARI

is_A075093(n)={isprime(n) & vecsort(Vec(Str(n)))==vecsort(Vec(Str(n=nextprime(n+1)))) & vecsort(Vec(Str(n)))==vecsort(Vec(Str(nextprime(n+1))))} \\ M. F. Hasler, Oct 11 2012

Python

from sympy import nextprime
from itertools import islice
def hash(n): return "".join(sorted(str(n)))
def agen(start=2): # generator of terms
    p = nextprime(start-1); q=nextprime(p); r=nextprime(q)
    hp, hq, hr = list(map(hash, [p, q, r]))
    while True:
        if hp == hq == hr: yield p
        p, q, r = q, r, nextprime(r)
        hp, hq, hr = hq, hr, hash(r)
print(list(islice(agen(), 3))) # Michael S. Branicky, Feb 19 2024