

A061715


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


3



4, 6, 12, 18, 30, 34, 42, 56, 60, 72, 86, 92, 94, 102, 108, 138, 142, 144, 150, 160, 180, 184, 186, 192, 198, 202, 204, 214, 216, 218, 220, 228, 236, 240, 248, 266, 270, 282, 300, 302, 304, 312, 320, 322, 328, 340, 348, 392, 394, 412, 414, 416, 420, 424, 432
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OFFSET

1,1


COMMENTS

The average of twin primes is a member. Is there ever a prime in the sequence?
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


LINKS

Table of n, a(n) for n=1..55.


EXAMPLE

34 is sandwiched between 33 and 35 which are of the form p*q where p and q are primes.


MAPLE

isA061715 := proc(n)
local nm1, np1 ;
nm1 := ifactors(n1)[2] ;
np1 := ifactors(n+1)[2] ;
if nops(nm1) = nops(np1) then
for i from 1 to nops(nm1) do
if op(2, op(i, nm1)) <> op(2, op(i, np1)) then
return false;
end if;
end do:
true ;
else
false;
end if;
end proc:
for n from 1 to 300 do
if isA061715(n) then
printf("%d, ", n);
end if;
end do: # R. J. Mathar, Jan 18 2017


MATHEMATICA

f[n_] := Flatten[Table[{ # [[2]]}] & /@ FactorInteger[n]]; Drop[ Select[ Range[415], Sort[f[ #  1]] == Sort[f[ # + 1]] & ], 1]


CROSSREFS

Cf. A074497, A074498.
Sequence in context: A130441 A068570 A074998 * A280469 A072570 A217259
Adjacent sequences: A061712 A061713 A061714 * A061716 A061717 A061718


KEYWORD

easy,nonn,changed


AUTHOR

Amarnath Murthy, Aug 21 2002


EXTENSIONS

Edited and extended by Robert G. Wilson v, Aug 22 2002


STATUS

approved



