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a(n) = smallest m such that A308190(m) = n, or -1 if no such m exists.
4

%I #47 Jun 24 2019 14:29:26

%S 5,6,8,7,10,16,17,30,29,54,53,102,101,198,197,390,389,774,773,1542,

%T 3080,3079,6154,12304,24604,36901,73798,147592,295180,295517,591030,

%U 1182056,1574849,3149694,4728211,6299383,12598762,25197520,25197533,50395062,100790120,100790119,201580234,403160464,806320924,1232145821,2464291638

%N a(n) = smallest m such that A308190(m) = n, or -1 if no such m exists.

%C It seems plausible that m exists for all n >= 0.

%C From _Chai Wah Wu_, Jun 14 2019: (Start)

%C All terms are even or prime. If a(n+1) is even, then 2*a(n)-a(n+1) = 4. a(n+1) <= 2*(a(n)-2) and thus m exists for all n >= 0. The proof in the comments of A308193 is applicable for this sequence as well.

%C If a(n) is prime, then a(n-1) <= a(n) + 1. For the prime terms 7, 17, 29, 53, 101, 197, 389, 773, 3079, 100790119, a(n-1) = a(n) + 1.

%C (End)

%H Chai Wah Wu, <a href="/A308191/b308191.txt">Table of n, a(n) for n = 0..54</a>

%Y Cf. A111234, A308190.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Jun 14 2019

%E a(24)-a(41) from _Chai Wah Wu_, Jun 14 2019

%E a(42)-a(44) from _Chai Wah Wu_, Jun 15 2019

%E a(45)-a(46) from _Chai Wah Wu_, Jun 16 2019