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]
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Aug 21 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Aug 22 2002
STATUS
approved