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A061715 Numbers which are sandwiched between two numbers having the same ordered canonical form.

%I A061715 #13 Jan 02 2020 04:14:48
%S A061715 4,6,12,18,30,34,42,56,60,72,86,92,94,102,108,138,142,144,150,160,180,
%T A061715 184,186,192,198,202,204,214,216,218,220,228,236,240,248,266,270,282,
%U A061715 300,302,304,312,320,322,328,340,348,392,394,412,414,416,420,424,432
%N A061715 Numbers which are sandwiched between two numbers having the same ordered canonical form.
%C A061715 The average of twin primes is a member. Is there ever a prime in the sequence?
%C A061715 The sequence does not contain odd numbers since the odd number would be sandwiched between 2k and 2k+2 = 2(k+1) for some k and one of k, k+1 is odd and the other even so the highest power of two dividing them cannot be the same.  Since 2 is not in the sequence, there can be no primes. - _Ray Chandler_, Apr 13 2019
%H A061715 Amiram Eldar, <a href="/A061715/b061715.txt">Table of n, a(n) for n = 1..10000</a>
%e A061715 34 is sandwiched between 33 and 35 which are of the form p*q where p and q are primes.
%p A061715 isA061715 := proc(n)
%p A061715     local nm1,np1 ;
%p A061715     nm1 := ifactors(n-1)[2] ;
%p A061715     np1 := ifactors(n+1)[2] ;
%p A061715     if nops(nm1) = nops(np1) then
%p A061715         for i from 1 to nops(nm1) do
%p A061715             if op(2,op(i,nm1)) <>  op(2,op(i,np1)) then
%p A061715                 return false;
%p A061715             end if;
%p A061715         end do:
%p A061715         true ;
%p A061715     else
%p A061715         false;
%p A061715     end if;
%p A061715 end proc:
%p A061715 for n from 1 to 300 do
%p A061715     if isA061715(n)  then
%p A061715         printf("%d,",n);
%p A061715     end if;
%p A061715 end do: # _R. J. Mathar_, Jan 18 2017
%t A061715 f[n_] := Flatten[Table[{ # [[2]]}] & /@ FactorInteger[n]]; Drop[ Select[ Range[415], Sort[f[ # - 1]] == Sort[f[ # + 1]] & ], 1]
%Y A061715 Cf. A074497, A074498.
%K A061715 easy,nonn
%O A061715 1,1
%A A061715 _Amarnath Murthy_, Aug 21 2002
%E A061715 Edited and extended by _Robert G. Wilson v_, Aug 22 2002