cp's OEIS Frontend

A370499 a(1) = 1; for n > 1, a(n) is smallest unused number such that a(n) is coprime to a(n-1), sopfr(a(n)) is coprime to sopfr(a(n-1)), Omega(a(n)) does not equal Omega(a(n-1)), the string length of a(n) does not equal the string length of a(n-1), and a(n) has no digit in common with a(n-1), where sopfr(k) is the sum of the primes dividing k, with repetition.

%I A370499 #12 Feb 21 2024 10:38:19
%S A370499 1,20,7,15,208,5,12,305,17,4,11,6,13,8,19,200,3,10,223,9,23,100,27,
%T A370499 101,22,103,24,107,25,104,29,105,2,45,109,26,113,28,111,40,117,32,147,
%U A370499 38,127,30,149,33,112,37,102,43,106,47,108,35,124,39,116,49,125,34,151,36,157,42,131,44,115
%N A370499 a(1) = 1; for n > 1, a(n) is smallest unused number such that a(n) is coprime to a(n-1), sopfr(a(n)) is coprime to sopfr(a(n-1)), Omega(a(n)) does not equal Omega(a(n-1)), the string length of a(n) does not equal the string length of a(n-1), and a(n) has no digit in common with a(n-1), where sopfr(k) is the sum of the primes dividing k, with repetition.
%C A370499 The fixed points begin 1, 2, 11, 13, 40, 357, 2353, 2393, 2465, 2473, 2529, 2649, 2767. It is unknown if the sequence is infinite.
%H A370499 Scott R. Shannon, <a href="/A370499/b370499.txt">Table of n, a(n) for n = 1..10000</a>
%e A370499 a(5) = 208 as a(4) = 15 and 208 is the smallest unused number that is coprime to 15, sopfr(208) = 21 is coprime to sopfr(15) = 8, Omega(208) = 5 does not equal Omega(15) = 2, the string length of "208" = 3 does not equal the string length of "15" = 2, and 208 has no digit in common with 15.
%o A370499 (Python)
%o A370499 from math import gcd
%o A370499 from sympy import factorint
%o A370499 from functools import cache
%o A370499 from itertools import count, islice
%o A370499 @cache
%o A370499 def sWd(n):
%o A370499     f = factorint(n)
%o A370499     return (sum(p*e for p,e in f.items()), sum(f.values()), str(n))
%o A370499 def agen(): # generator of terms
%o A370499     yield 1
%o A370499     aset, an, mink = {1, 20}, 20, 2
%o A370499     while True:
%o A370499         yield an
%o A370499         s, W, d = sWd(an)
%o A370499         an = next(k for k, sk, Wk, dk in ((k,)+sWd(k) for k in count(mink)) if k not in aset and gcd(k, an)==1 and gcd(sk, s)==1 and Wk!=W and len(dk)!=len(d) and set(dk)&set(d)==set())
%o A370499         aset.add(an)
%o A370499         while mink in aset: mink += 1
%o A370499 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Feb 21 2024
%Y A370499 Cf. A001414, A001222, A370496, A370047, A370497, A064413, A277272, A027748.
%K A370499 nonn,base
%O A370499 1,2
%A A370499 _Scott R. Shannon_, Feb 20 2024