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

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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(n-1)[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: A109290 A130441 A074998 * A280469 A353073 A072570

Adjacent sequences: A061712 A061713 A061714 * A061716 A061717 A061718

Keyword

easy,nonn

Author

Amarnath Murthy, Aug 21 2002

Extensions

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

Status

approved