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%I #11 Sep 02 2023 04:11:19
%S 3,1,16,192,768,3072,12288,49152,196608,786432,3145728,12582912,
%T 50331648,201326592,805306368,3221225472,12884901888,51539607552
%N Smallest m such that |A259029(m)| = n.
%C |A259029(a(n))| = n and |A259029(m)| != n for m < a(n).
%e . n | a(n) | A259029(a(n)) | A259024(a(n))
%e . ----+------------------------+---------------+--------------
%e . 0 | 3 | 3*2^0 | 0 | -1
%e . 1 | 1 | 2^0 | 1 | 1
%e . 2 | 16 | 2^4 | 2 | 1
%e . 3 | 192 | 3*2^6 | -3 | -1
%e . 4 | 768 | 3*2^8 | -4 | -1
%e . 5 | 3072 | 3*2^10 | -5 | -1
%e . 6 | 12288 | 3*2^12 | -6 | -1
%e . 7 | 49152 | 3*2^14 | -7 | -1
%e . 8 | 196608 | 3*2^16 | -8 | -1
%e . 9 | 786432 | 3*2^18 | -9 | -1
%e . 10 | 3145728 | 3*2^20 | -10 | -1
%e . 11 | 12582912 | 3*2^22 | -11 | -1
%e . 12 | 50331648 | 3*2^24 | -12 | -1
%e . 13 | 201326592 | 3*2^26 | -13 | -1
%e . 14 | 805306368 | 3*2^28 | -14 | -1
%e . 15 | 3221225472 | 3*2^30 | -15 | -1
%e . 16 | 12884901888 | 3*2^32 | -16 | -1
%e . 17 | 51539607552 | 3*2^34 | -17 | -1 .
%o (Haskell)
%o import Data.List (elemIndex); import Data.Maybe (fromJust)
%o a259031 = (+ 1) . fromJust . (`elemIndex` (map abs a259029_list))
%o (PARI) g(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i,1]; e = f[i,2]; if(p == 2, (1 + (-1)^e)/2, if(p==3, if(e==1, -1, 0), if(p%6 == 1, 1, (-1)^e))));} \\ A259029
%o lista(len) = {my(v=vector(len), s=0, t, k=1, c=0); while(c < len, s += g(k); t = abs(s)+1; if(t <= len && v[t] == 0, c++; v[t] = k); k++); v} \\ _Amiram Eldar_, Sep 02 2023
%Y Cf. A259029, A259024.
%K nonn
%O 0,1
%A _Reinhard Zumkeller_, Jun 17 2015
%E a(12)-a(17) from _Amiram Eldar_, Sep 02 2023