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A127929
a(n) = A127928(n) mod 18.
2
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, 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, 1, 1, 7, 1, 7, 1, 1, 7, 1, 7, 1, 7, 1, 7, 7, 7, 7, 7, 1
OFFSET
1,1
COMMENTS
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.
LINKS
Douglas J. Shaw, The Pure Numbers Generated by the Collatz Sequence, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, p. 194.
FORMULA
Pure hailstone (Collatz) numbers that are also prime (i.e. the set A127928), mod 18.
EXAMPLE
a(5) = 7 since A127928(5) = 43 and 43 == 7 mod 18.
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Feb 07 2007
EXTENSIONS
More terms from Amiram Eldar, Feb 28 2020
STATUS
approved