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Nearest integer to exponential integral of n.
(Formerly M1378 N0538)
1

%I M1378 N0538 #30 Nov 20 2023 08:19:29

%S 2,5,10,20,40,86,192,440,1038,2492,6071,14960,37198,93193,234956,

%T 595561,1516638,3877904,9950907,25615653,66127186,171144671,443966370,

%U 1154115392,3005950907,7842940992,20496497120,53645118592,140599195758

%N Nearest integer to exponential integral of n.

%D W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables).

%D A. Fletcher, J. C. P. Miller, L. Rosenhead, and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 267.

%D J. W. L. Glaisher, Phil. Trans. Royal Society, 160 (1870), 367-388.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A002460/b002460.txt">Table of n, a(n) for n = 1..1000</a>

%F Ei(x) = Integral_{-oo..x} (e^t/t) dt.

%F a(n) ~ exp(n)/n. - _Vaclav Kotesovec_, May 23 2014

%t a[n_] := Round[ExpIntegralEi[n]]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Dec 19 2011 *)

%o (PARI) a(n)=round(-eint1(-n))

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_