Hmm . without getting too mystical - 7, 19, 37, 61, and 91 hydrogen atoms.. can you predict the next inferred number, based on six-fold symmetry ? It could be the most important since it relates to the square of six.
It looks to me like it would be 127. With a six-fold symmetry every progressive step is itself multiplied by six and added to the previous form - so by my calculation it would be (6*6) + 91 = 127. This is somewhat curious in itself, as 7 and 127 are Mersenne primes but the others are not. Also hydrogen definitely prefers this kind of symmetry as we know from snow and ice crystals. This has a strange connection to Greek mysticism, FWIW and maybe more . Mersenne primes were studied by Euclid, who found a connection to the so-called perfect numbers (although no odd or prime can also be perfect, by definition). Not sure what it all means . or if it has one iota of practical value . Jones From: Axil Axil http://cdsweb.cern.ch/record/974281/files/0607193.pdf * These planar clusters have six-fold symmetry and contain 7, 19, 37, 61, or 91 hydrogen atoms. These numbers are the so called magic numbers for closed-pack clusters.
