This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127929 #15 Jan 05 2025 19:51:38 %S A127929 3,7,1,1,7,1,7,7,1,1,7,1,1,1,7,7,1,7,1,7,7,7,7,1,1,7,7,7,1,1,1,7,7,1, %T A127929 7,1,7,7,7,7,1,1,1,7,1,7,1,7,1,7,7,7,7,1,7,1,7,7,7,1,1,7,7,1,7,7,1,7, %U A127929 1,1,7,1,7,1,1,7,1,7,1,7,1,7,7,7,7,7,1 %N A127929 a(n) = A127928(n) mod 18. %C A127929 Aside from "3", all terms of A127928 must be 1 or 7 mod 18 (see A127928 for mod rules); but not all primes mod 1 or 7 are pure hailstone numbers. For example, the prime 61 == 7 mod 18 but 61 is impure. Conjecture: for large n, the numbers of 1 and 7 mod 18 terms are approximately equal. %H A127929 Amiram Eldar, <a href="/A127929/b127929.txt">Table of n, a(n) for n = 1..10000</a> %H A127929 Douglas J. Shaw, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/44-3/quartshaw03_2006.pdf">The Pure Numbers Generated by the Collatz Sequence</a>, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, p. 194. %F A127929 Pure hailstone (Collatz) numbers that are also prime (i.e. the set A127928), mod 18. %e A127929 a(5) = 7 since A127928(5) = 43 and 43 == 7 mod 18. %Y A127929 Cf. A127928, A127930, A061641, A127633, A006577, A066903. %K A127929 nonn %O A127929 1,1 %A A127929 _Gary W. Adamson_, Feb 07 2007 %E A127929 More terms from _Amiram Eldar_, Feb 28 2020