A393164 Greatest common divisors of consecutive terms of numbers of the form 2^i*5^j.

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, Table of n, a(n) for n = 1..10000

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

Cf. A003592, A112752, A186711.

Sequence in context: A361933 A381629 A036863 * A209270 A083698 A128976

Adjacent sequences: A393161 A393162 A393163 * A393165 A393166 A393167

Keyword

nonn,easy,look

Author

Michael De Vlieger, Mar 04 2026

Status

approved