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URL: https://oeis.org/A393164

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A393164
Greatest common divisors of consecutive terms of numbers of the form 2^i*5^j.
3
1, 2, 1, 1, 2, 2, 4, 5, 1, 8, 10, 2, 16, 20, 25, 1, 32, 40, 50, 2, 64, 80, 100, 4, 1, 5, 160, 200, 8, 2, 10, 320, 400, 16, 4, 20, 5, 25, 800, 32, 8, 40, 10, 50, 1600, 64, 16, 80, 20, 100, 25, 125, 128, 32, 160, 40, 200, 50, 250, 256, 64, 320, 80, 400, 100, 500
OFFSET
1,2
COMMENTS
All terms are elements of A003592. - Chai Wah Wu, Mar 09 2026
LINKS
Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.
FORMULA
a(n) = gcd(A003592(n), A003592(n+1)).
MATHEMATICA
s = With[{n = 10^5}, Union@ Flatten@ Table[2^i*5^j, {i, 0, Log2[n]}, {j, 0, Log[5, n/2^i] } ] ]; MapApply[GCD, Partition[s, 2, 1] ]
PROG
(Python)
from math import gcd
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A393164(n):
def f(x): return n+x-sum((x//5**i).bit_length() for i in range(integer_log(x, 5)[0]+1))
return gcd(m:=bisection(f, n, n), bisection(lambda x:f(x)+1, m, m)) # Chai Wah Wu, Mar 09 2026
(PARI) a(n)= my(m=5, p=0, r=List([1]), v); while(#r<=n, while((v=r[p++]*2)<m, listput(~r, v)); listput(~r, m); listput(~r, v); m*=5); gcd(r[n], r[n+1]); \\ Ruud H.G. van Tol, Mar 09 2026
CROSSREFS
KEYWORD
nonn,easy,look
AUTHOR
Michael De Vlieger, Mar 04 2026
STATUS
approved