A227844 Lexicographically earliest sequence whose second differences are the digits of Pi.

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

Offset

1,3

Comments

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.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..20002

Crossrefs

Cf. A000796, A226930.

Sequence in context: A185440 A134467 A178132 * A191595 A047882 A184260

Adjacent sequences: A227841 A227842 A227843 * A227845 A227846 A227847

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 20 2013, Aug 21 2013

Status

approved