The first, 40, terms of the sequence enumerating permutations of length n suc\
    h that pi[i+2]-pi[i] is never 5 are



            or equivalently, such that pi[i+5]-pi[i] is never 2 are

[1, 2, 6, 24, 120, 624, 3924, 28872, 243000, 2300400, 24167568, 279023304, 
3509619516, 47753201520, 698671018800, 10935962501040, 182320112891244, 
3225007044151920, 60320872398593520, 1189409881438465200, 24657336563892214320,
536107748312711193840, 12198034660050905063760, 289858734809832170896560, 
7180316976935747731993200, 185109690046459699927614960, 
4958706722719910677688255760, 137828173626994026054443952240, 
3969720768097901037099011022000, 118330586164337120152004632057200, 
3646266086813819503966075150279920, 116023515934738573719029204441259120, 
3808480511633067964784081576769944400, 128841024534553338234186345524240459760,
4488140988744565253410974825600082714800, 
160851176655965581555879890019442493084720, 
5926297255727660595250862826998126466545040, 
224294615923873615246072243802109056486425200, 
8714100393025508666647261303224097811914623600, 
347298216862180671807628947335967345820465086000]


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