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%I #5 Mar 31 2012 13:46:52
%S 1,9,15,25,39,51,55,75,91,112,130,152,176,202,230,260,287,319,352,386,
%T 422,460,495,535,579,621,666,712,760,810,862,916,965,1022,1078,1136,
%U 1196,1258,1322,1385,1450,1516,1584,1653,1725,1795,1869,1945,2022,2100
%N Sequence with properties that a(1)=1, no prime appears in the sequence or the first differences and all other integers exactly once (in sequence or first differences).
%C Sequence and first differences are:
%C 1.9.15..25..39..51.55..75..91...
%C .8.6..10..14..12..4..20..16.. etc.
%e Start with a(1)=1; what can we add to produce a(2)? Not 1 (already used), not 2 or 3 (primes), not 4 (produces 5, which is prime), not 6 (produces 7, which is prime) -- 8 is ok and produces 9 (1+8) which is not prime, so a(2) =9; what can we add to a(2) to produce a(3)? Not 1, 2 or 3 (see above), not 4 (produces 13, which is prime), not 5 (prime) -- 6 is ok and produces 15 (9+6), which is not prime, so a(3)=15; what can we add to a(3) to produce a(4)? Not 1, 2 and 3 (see above), not 4 (produces 19, which is prime), not 5 (prime), not 6 (already used), not 7 (prime), not 8 or 9 (already used) -- 10 is ok and produces 25 (15+10), which is not prime, so a(4)=25; etc.
%K easy,nonn
%O 1,2
%A _Eric Angelini_, Aug 31 2005
%E Corrected and extended by _Ray Chandler_, Sep 02 2005