A002850 Number of decompositions of 2n into sum of 2 lucky numbers. (Formerly M0071 N0023)

1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 2, 2, 3, 2, 2, 4, 2, 3, 4, 2, 3, 5, 1, 4, 5, 2, 3, 5, 1, 3, 5, 3, 3, 5, 3, 5, 7, 3, 5, 7, 4, 4, 7, 3, 3, 7, 4, 3, 9, 5, 3, 7, 5, 3, 8, 5, 4, 8, 5, 3, 7, 5, 3, 9, 4, 3, 12, 6, 4, 12, 6, 4, 10, 6, 4, 8, 5, 5, 8, 7, 5, 11, 5, 4

Offset

1,5

Comments

In general, a(3n-1) is larger than a(3n-2) and a(3n), which explains the bimodal nature of the graph. - T. D. Noe, Jan 29 2007

References

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

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

M. L. Stein and P. R. Stein, Tables of the Number of Binary Decompositions of All Even Numbers Less Than 200,000 into Prime Numbers and Lucky Numbers. Report LA-3106, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Sep 1964.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

V. Gardiner, R.Lazarus, N. Metropolis and S. Ulam, On certain sequences of integers defined by sieves, Math. Mag., 29 (1955), 117-119.

Mathematica

nmax = 1000;
luckies = Table[2i+1, {i, 0, nmax}]; For[n = 2, n < Length[luckies], r = luckies[[n++]]; luckies = ReplacePart[luckies, Table[r*i -> Nothing, {i, 1, Length[luckies]/r}]]];
a[n_] := IntegerPartitions[2n, {2}, luckies] // Length;
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Aug 03 2022, after Robert Israel in A000959 *)

Crossrefs

Cf. A000959.

Sequence in context: A345933 A198325 A293909 * A355248 A111944 A109814

Adjacent sequences: A002847 A002848 A002849 * A002851 A002852 A002853

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

Paul Zimmermann points out that the second term was incorrectly given as 2 in the Encyclopedia of Integer Sequences.

Missing a(71)-a(73) inserted by Sean A. Irvine, Nov 05 2014

Status

approved