A394408 - OEIS

%I #10 Mar 29 2026 04:30:25

%S 1,4,5,25,125,512,65536,8388608,1073741824,137438953472,

%T 17592186044416,2251799813685248,288230376151711744,

%U 36893488147419103232,4656612873077392578125,173472347597680709441192448139190673828125,6427752177035961102167848369364650410088811975131171341205504

%N Lesser of two consecutive numbers of the form 2^i*5^j with i, j >= 0, that are coprime.

%H Michael De Vlieger, <a href="/A394408/b394408.txt">Table of n, a(n) for n = 1..23</a>

%H Michael De Vlieger, <a href="/A394408/a394408.txt">Extended table of n, s(i), a(n), b(n)</a> for n = 1..29, where b = A394452 and s = A003592.

%e Let s = A003592 and b = A394452.

%e Table of n, a(n) for n = 1..12:

%e  n          a(n)     b(n)

%e ----------------------------

%e  1     s(1) = 1        2

%e  2     s(3) = 2^2      5

%e  3     s(4) = 5        2^3

%e  4     s(9) = 5^2      2^5

%e  5    s(16) = 5^3      2^7

%e  6    s(25) = 2^9      5^4

%e  7    s(68) = 2^16     5^7

%e  8   s(132) = 2^23     5^10

%e  9   s(217) = 2^30     5^13

%e 10   s(323) = 2^37     5^16

%e 11   s(450) = 2^44     5^19

%e 12   s(598) = 2^51     5^22

%p M:= 10^80: # for terms <= M

%p L:= sort([seq(seq(2^i*5^j,i=0..floor(log[2](M/5^j))),j=0..floor(log[5](M)))]):

%p L[select(t -> igcd(L[t],L[t+1])=1, [$1..nops(L)-1])]; # _Robert Israel_, Mar 23 2026

%t s = With[{nn = 10^80}, Union@ Flatten@ Table[2^i* 5^j, {i, 0, Log2[nn]}, {j, 0, Log[5, nn/2^i] } ] ]; Select[Partition[s, 2, 1], CoprimeQ @@ # &][[;; , 1]]

%Y Cf. A003592, A186927, A393164, A394452.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Mar 20 2026