The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A350553 a(n) is the smallest number k for which A000120(k) = A000120(k') = n, or -1 if no such k exists, where k' is the arithmetic derivative of k (A003415). 0
 0, 2, 6, 22, 27, 110, 175, 502, 894, 2037, 3775, 8182, 24558, 49142, 98286, 196598, 655323, 524278, 2088950, 2097142, 6291438, 16515062, 15728575, 62914175, 100663278, 134217718, 528482294, 939524086, 2145386486, 3221225454, 11811159998, 8589934582, 47244640246 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture. a(n) >= 0 for all n. LINKS Table of n, a(n) for n=0..32. EXAMPLE 0' = 0, A000120(0) = A000120(0') = 0, so a(0) = 0. 1' = 0, A000120(1) = 1, A000120(1') = 0. 2 = 10_2, 2' = 1 = 1_0, so A000120(2) = A000120(2') = 1 and a(1) = 2. MATHEMATICA bw[n_] := DigitCount[n, 2, 1]; d[0] = d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); seq[m_, nmax_] := Module[{s = Table[-1, {m + 1}], c = 0, n = 0, i}, While[c < m + 1 && n < nmax, i = bw[n] + 1; If[i <= m && s[[i]] < 0, If[bw[d[n]] + 1 == i, c++; s[[i]] = n]]; n++]; TakeWhile[s, # > -1 &]]; seq[16, 10^6] (* Amiram Eldar, Jan 27 2022 *) PROG (Magma) f:=func; a:=[]; for n in [0..22] do k:=2^n-1 ; while &+Intseq(k, 2) ne n or &+Intseq( Floor(f(k)), 2) ne n do k:=k+1; end while; Append(~a, k*1); end for; a; (PARI) d(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415 a(n) = my(k=2^n-1); while ((hammingweight(k) != n) || (hammingweight(d(k)) != n), k++); k; \\ Michel Marcus, Jan 25 2022 CROSSREFS Cf. A000120, A003415, A350552. Sequence in context: A085286 A062085 A284632 * A325020 A335131 A147800 Adjacent sequences: A350550 A350551 A350552 * A350554 A350555 A350556 KEYWORD nonn,base AUTHOR Marius A. Burtea, Jan 24 2022 EXTENSIONS a(30)-a(32) from Jinyuan Wang, Jan 27 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 10:38 EST 2023. Contains 367722 sequences. (Running on oeis4.)