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A267824 Composite numbers n such that binomial(2n-1, n-1) == 1 (mod n^2). 6
283686649, 4514260853041 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Babbage proved the congruence holds if n > 2 is prime.
See A088164 and A263882 for references, links, and additional comments.
Conjecture: n is a term if and only if n = A088164(i)^2 for some i >= 1 (cf. McIntosh, 1995, p. 385). - Felix Fröhlich, Jan 27 2016
The "if" part of the conjecture is true: see the McIntosh reference. - Jonathan Sondow, Jan 28 2016
The above conjecture implies that this sequence and A228562 are disjoint. - Felix Fröhlich, Jan 27 2016
Composites c such that A281302(c) > 1. - Felix Fröhlich, Feb 21 2018
LINKS
Richard J. McIntosh, On the converse of Wolstenholme's Theorem, Acta Arithmetica, 71 (1995), 381-389.
J. Sondow, Extending Babbage's (non-)primality tests, in Combinatorial and Additive Number Theory II, Springer Proc. in Math. & Stat., Vol. 220, 269-277, CANT 2015 and 2016, New York, 2017; arXiv:1812.07650 [math.NT], 2018.
EXAMPLE
a(1) = 16843^2 and a(2) = 2124679^2 are squares of Wolstenholme primes A088164.
CROSSREFS
Sequence in context: A017362 A017482 A017614 * A185428 A320878 A320879
KEYWORD
nonn,bref,hard,more
AUTHOR
Jonathan Sondow, Jan 25 2016
STATUS
approved

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Last modified April 18 03:33 EDT 2024. Contains 371767 sequences. (Running on oeis4.)