# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a337376 Showing 1-1 of 1 %I A337376 #32 Jul 08 2021 14:22:03 %S A337376 1,2,3,4,5,3,9,8,7,10,5,6,25,9,27,16,11,14,21,20,7,5,15,12,49,50,25,9, %T A337376 125,27,81,32,13,22,33,28,55,21,63,40,11,14,7,10,35,15,45,24,121,98, %U A337376 147,100,49,25,25,18,343,250,125,27,625,81,243,64,17,26,39,44,65,33,99,56,91,110,55,42,275,63,189,80,13,22 %N A337376 Primorial deflation (numerator) of Doudna-tree. %C A337376 Tree with both numerators (this sequence) and denominators (A337377) shown starts as: %C A337376 1/1 %C A337376 | %C A337376 2 %C A337376 - %C A337376 1 %C A337376 3 / \ 4 %C A337376 - ................. ................. - %C A337376 2 1 %C A337376 5 / \ 3 9 / \ 8 %C A337376 - ....... ....... - - ....... ....... - %C A337376 3 1 4 1 %C A337376 / \ / \ / \ / \ %C A337376 / \ / \ / \ / \ %C A337376 / \ / \ / \ / \ %C A337376 7 10 5 6 25 9 27 16 %C A337376 - -- - - -- - -- -- %C A337376 5 3 2 1 9 2 8 1 %C A337376 / \ / \ / \ / \ / \ / \ / \ / \ %C A337376 11 14 21 20 7 5 15 12 49 50 25 9 125 27 81 32 %C A337376 -- -- -- -- - - -- -- -- -- -- - --- -- -- -- %C A337376 7 5 10 3 3 1 4 1 25 9 6 1 27 4 16 1 %C A337376 etc. %H A337376 Antti Karttunen, Table of n, a(n) for n = 0..8191 %H A337376 Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537 %H A337376 Index entries for fraction trees %F A337376 a(n) = A319626(A005940(1+n)). %F A337376 a(n) = A005940(1+n) / A337375(n). %F A337376 a(2*n) = A003961(a(n)). %F A337376 If A007814(n+1) < A337821(n+1) then a(2*n+1) = a(n), otherwise a(2*n+1) = 2 * a(n). %F A337376 If A337377(n) mod 2 = 0 then a(2*n+1) = a(n), otherwise a(2*n+1) = 2 * a(n). %F A337376 A000265(a(2*n+1)) = A000265(a(n)). %F A337376 A001222(a(2*n)) = A001222(A337377(2*n)) = A001222(a(n)). %F A337376 A001222(a(2*n+1)) - A001222(A337377(2*n+1)) = 1 + A001222(a(n)) - A001222(A337377(n)). %t A337376 Array[#1/GCD[#1, #2] & @@ {#, Apply[Times, Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger[#]]]} &@ Function[p, Times @@ Flatten@ Table[Prime[Count[Flatten[#], 0] + 1]^#[[1, 1]] &@ Take[p, -i], {i, Length[p]}]]@ Partition[Split[Join[IntegerDigits[# - 1, 2], {2}]], 2] &, 82] (* _Michael De Vlieger_, Aug 27 2020 *) %o A337376 (PARI) %o A337376 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); }; %o A337376 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)}; %o A337376 A319626(n) = (n / gcd(n, A064989(n))); %o A337376 A337376(n) = A319626(A005940(1+n)); %Y A337376 A005940, A319626, A337375 are used in a formula defining this sequence. %Y A337376 Cf. A064989. %Y A337376 Cf. A337377 (denominators). %Y A337376 A000265, A001222, A003961, A007814, A337821 are used to express relationship between terms of this sequence. %Y A337376 Cf. also A329886, A346096. %K A337376 nonn,frac,tabf,look %O A337376 0,2 %A A337376 _Antti Karttunen_, _Michael De Vlieger_ and _Peter Munn_, Aug 25 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE