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A227844
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Lexicographically earliest sequence whose second differences are the digits of Pi.
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2
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0, 1, 5, 10, 19, 29, 44, 68, 94, 126, 163, 203, 248, 301, 363, 432, 510, 591, 674, 760, 854, 952, 1056, 1162, 1274, 1390, 1509, 1631, 1761, 1894, 2029, 2171, 2322, 2478, 2634, 2792, 2958, 3132, 3310, 3489, 3677, 3872, 4068, 4270, 4481, 4695, 4918, 5150, 5385, 5627, 5874, 6122, 6370, 6623, 6884, 7147, 7410, 7682, 7961, 8244, 8536, 8832, 9132, 9437
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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If the digits of Pi were random, and the digits of A226930 were also random, this sequence would have the same rate of growth as A226930. This is certainly not true for the initial terms. Here are histograms of the first 20000 digits of Pi and the second differences of A226930:
# of 0s 1s 2s 3s 4s 5s 6s 7s 8s 9s
Pi: [1954, 1997, 1986, 1987, 2043, 2082, 2017, 1953, 1961, 2020]
A226930: [1766, 2859, 2066, 2082, 1991, 1911, 1937, 1847, 1795, 1746] (Note the excessive fraction of 1s)
So although both sequences appear to grow like C*n*(n+1)/2, the growth of A226930 is initially rather slower than that of A227844.
For large n it seems likely that A226930(n)/A227844(n) will approach 1.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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