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 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. 1
 1, 20, 7, 15, 208, 5, 12, 305, 17, 4, 11, 6, 13, 8, 19, 200, 3, 10, 223, 9, 23, 100, 27, 101, 22, 103, 24, 107, 25, 104, 29, 105, 2, 45, 109, 26, 113, 28, 111, 40, 117, 32, 147, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Scott R. Shannon, Table of n, a(n) for n = 1..10000 EXAMPLE 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. PROG (Python) from math import gcd from sympy import factorint from functools import cache from itertools import count, islice @cache def sWd(n): f = factorint(n) return (sum(p*e for p, e in f.items()), sum(f.values()), str(n)) def agen(): # generator of terms yield 1 aset, an, mink = {1, 20}, 20, 2 while True: yield an s, W, d = sWd(an) 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()) aset.add(an) while mink in aset: mink += 1 print(list(islice(agen(), 70))) # Michael S. Branicky, Feb 21 2024 CROSSREFS Cf. A001414, A001222, A370496, A370047, A370497, A064413, A277272, A027748. Sequence in context: A076594 A174991 A217418 * A196102 A196099 A102409 Adjacent sequences: A370496 A370497 A370498 * A370500 A370501 A370502 KEYWORD nonn,base AUTHOR Scott R. Shannon, Feb 20 2024 STATUS approved

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Last modified June 22 12:33 EDT 2024. Contains 373571 sequences. (Running on oeis4.)