The first, 40, terms of the sequence enumerating permutations of length n suc\
    h that pi[i+3]-pi[i] is never 5 are



            or equivalently, such that pi[i+5]-pi[i] is never 3, are

[1, 2, 6, 24, 120, 648, 4140, 30624, 258048, 2440320, 25575432, 294579936, 
3696916704, 50193365952, 732874685760, 11449410148224, 190535561333568, 
3364607458730880, 62831761039377984, 1237070353963472640, 25609485055819680000,
556079014498954710528, 12636858676373038090752, 299938993470832215133440, 
7421938409336391322940160, 191142680054948627730304320, 
5115371547379381273857350880, 142053029209670549556331592160, 
4087877741026536072204865241280, 121753222860217367846538990095040, 
3748831318546325762887597165030080, 119199621671052293866922869679543520, 
3910010205780464814165525284587356000, 132188135474458014769343383078808750400,
4601832178741036349715351245526453365760, 
164826633167513935718229487849489430065920, 
6069283948589757903343449806208440162545440, 
229580492061188108173550591022137673095518560, 
8914793877292337560646638014001986640924001280, 
355118872315389607691338351518713619951083216640]


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                         This took, 1554.341, seconds.