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

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

Author

Michael De Vlieger, Dec 06 2021

Keywords

• nonn

Comments

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

Records are A008578.

Links

• 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

Crossrefs

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

Programs

Mathematica

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]]

Python

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