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A256994 a(n) = n + 1 when n <= 3, otherwise a(n) = 2^(n-2) + 3; also iterates of A005187 starting from a(1) = 2.

%I A256994 #19 Feb 22 2025 16:13:06
%S A256994 2,3,4,7,11,19,35,67,131,259,515,1027,2051,4099,8195,16387,32771,
%T A256994 65539,131075,262147,524291,1048579,2097155,4194307,8388611,16777219,
%U A256994 33554435,67108867,134217731,268435459,536870915,1073741827,2147483651,4294967299,8589934595,17179869187,34359738371,68719476739,137438953475,274877906947
%N A256994 a(n) = n + 1 when n <= 3, otherwise a(n) = 2^(n-2) + 3; also iterates of A005187 starting from a(1) = 2.
%C A256994 Note that if we instead iterated function b(n) = 1+A005187(n), from b(1) onward, we would get the powers of two, A000079.
%H A256994 Antti Karttunen, <a href="/A256994/b256994.txt">Table of n, a(n) for n = 1..128</a>
%F A256994 If n < 4, a(n) = n + 1, otherwise a(n) = 2^(n-2) + 3 = A062709(n-2).
%F A256994 a(1) = 2; for n > 1, a(n) = A005187(a(n-1)).
%t A256994 Table[If[n<4,n+1,2^(n-2)+3],{n,40}] (* _Harvey P. Dale_, May 14 2019 *)
%o A256994 (PARI)
%o A256994 A256994(n) = if(n < 4, n+1, 2^(n-2) + 3);
%o A256994 (PARI)
%o A256994 \\ By iterating A005187:
%o A256994 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A256994 i=1; k=2; print1(k); while(i <= 40, k = A005187(k); print1(", ", k); i++);
%o A256994 (Scheme)
%o A256994 (define (A256994 n) (if (< n 4) (+ n 1) (+ (A000079 (- n 2)) 3)))
%o A256994 (Scheme)
%o A256994 ;; The following uses memoization-macro definec:
%o A256994 (definec (A256994 n) (if (= 1 n) 2 (A005187 (A256994 (- n 1)))))
%Y A256994 Topmost row of A256995, leftmost column of A256997.
%Y A256994 Cf. A000079, A005187, A062709, A068156.
%K A256994 nonn
%O A256994 1,1
%A A256994 _Antti Karttunen_, Apr 15 2015