A073734 -id:A073734 - cp's OEIS frontend

A387087 GCD of pairs of consecutive terms of the sequence A386482.

1, 2, 2, 3, 3, 3, 2, 2, 2, 7, 7, 3, 2, 4, 5, 5, 5, 5, 2, 2, 2, 2, 11, 11, 3, 9, 2, 2, 2, 19, 19, 3, 2, 2, 2, 2, 2, 2, 2, 5, 5, 3, 13, 13, 5, 2, 2, 7, 7, 3, 17, 17, 2, 2, 2, 31, 31, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 3, 23, 23, 2, 47, 47, 3, 2, 2, 2, 2, 2

Offset: 1

Rémy Sigrist, Aug 16 2025

nonn

			The first terms, alongside the first terms of A386482, are:
  n   a(n)  A386482(n)
  --  ----  ----------
   1     1           1
   2     2           2
   3     2           4
   4     3           6
   5     3           3
   6     3           9
   7     2          12
   8     2          10
   9     2           8
  10     7          14
  11     7           7
  12     3          21
  13     2          18
  14     4          16

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A073734, A386482.

PARI
```
\\ See Links section.
```

a(n) = gcd(A386482(n), A386482(n+1)).

A348470 a(n) = lpf(EKG(n)) = A020639(A064413(n)).

Original entry on oeis.org

1, 2, 2, 2, 3, 3, 2, 2, 2, 5, 3, 2, 2, 7, 3, 2, 2, 2, 2, 11, 3, 3, 2, 5, 5, 2, 2, 13, 3, 2, 2, 2, 17, 3, 2, 2, 19, 3, 3, 2, 2, 2, 23, 3, 2, 2, 2, 2, 2, 7, 3, 2, 5, 5, 2, 2, 29, 3, 2, 2, 31, 3, 2, 2, 2, 2, 37, 3, 3, 2, 2, 2, 2, 41, 3, 3, 2, 7, 2, 2, 43, 3, 2, 5

Offset: 1

Michael De Vlieger, Dec 06 2021

nonn

Prime p_n appears first at a(A064955(n)).

Records are A008578.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Michael De Vlieger, Log-log scatterplot of a(n) for n=1..2^12.
Michael De Vlieger, Log-log scatterplot of a(n) for n=1..2^18.
Index entries for sequences related to EKG sequence

Cf. A000040, A008578, A020639, A064413, A064955, A073734.

Map[FactorInteger[#][[1, 1]] &, Nest[Block[{k = 3}, While[Or[MemberQ[#, k], GCD[#[[-1]], k] == 1], k++]; Append[#, k]] &, {1, 2}, 84]]
(* or, faster *)
s = {1, 2}; u = 3; c[_] = 0; Set[j, 2]; Array[Set[c[#], #] &, 2]; Range[2]~Join~Reap[Do[If[PrimeQ[j], Set[u, NextPrime[u]]]; Set[k, u]; Which[And[PrimeQ[j], OddQ[j]], Set[k, 3 j], And[PrimeQ[j/2], OddQ[j/2]], Set[k, j/2], True, While[Nand[c[k] == 0, GCD[j, k] > 1], k++]]; Sow[FactorInteger[k][[1, 1]] ]; Set[c[k], i]; j = k, {i, 4, 10^4}]][[-1, -1]]

from itertools import islice, count
from math import gcd
from sympy import primefactors
def A064413gen(): # generator of terms
    yield 1
    yield 2
    l, s, b = 2, 3, set()
    for _ in count(0):
        i = s
        while True:
            if not i in b and gcd(i,l) > 1:
                yield i
                l = i
                b.add(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
            i += 1
def A348470(n): return 1 if n == 1 else min(primefactors(next(islice(A064413gen(),n-1,None)))) # Chai Wah Wu, Dec 07 2021

cp's OEIS Frontend

A387087 GCD of pairs of consecutive terms of the sequence A386482.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula