A039952 Maximum cardinality of finite D0L sequence over an alphabet with n symbols.

1, 2, 3, 4, 5, 6, 7, 12, 15, 20, 30, 31, 60, 61, 84, 105, 140, 210, 211, 420, 421, 422, 423, 840, 841, 1260, 1261, 1540, 2310, 2520, 4620, 4621, 5460, 5461, 9240, 9241, 13860, 13861, 16380, 16381, 27720, 30030, 32760, 60060, 60061, 60062, 60063, 120120, 120121

Offset

0,2

References

P. M. B. Vitanyi, Lindenmayer Systems: Structure, Languages and Growth Functions, Mathematisch Centrum, Math. Centre Tracts #96, 1980, p. 25.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

O. Osterby, Prime decompositions with minimum sum, Matematisk Institut, Aarhus Universitet, Technical Report DAIMI PB-19, November 1973; see the third column of Table 5 on page 18.

O. Osterby, Prime decompositions with minimum sum, Nordisk Tidskr. Informationsbehandling (BIT) 16 (1976), 451-458.

Formula

Max { Prod p^a + d : Sum p^a + d = n }, p prime.

a(n) = max(a(n-1)+1, A051703(n)). - Andrew Howroyd, Jan 05 2018

Example

a(11) = 31 because we can write 11 = 1 + 2 + 3 + 5 and 31 = 1+2*3*5.

Prog

(PARI) \\ here s is A051703 as a vector
s(n)={my(v=vector(n+1)); v[1]=1; forprime(p=2, n, forstep(i=#v, 1, -1, my(q=1); while(q*p<i, q*=p; v[i]=max(v[i], q*v[i-q])))); v}
seq(n)={my(v=s(n)); for(i=2, #v, v[i]=max(v[i], v[i-1]+1)); v} \\ Andrew Howroyd, Jan 05 2018

Crossrefs

Cf. A051703.

Sequence in context: A353725 A108948 A107818 * A129978 A251556 A200446

Adjacent sequences: A039949 A039950 A039951 * A039953 A039954 A039955

Keyword

nonn

Author

Jeffrey Shallit

Extensions

First 4 values appear incorrectly in cited references; corrected by JOS

a(0)=1 and terms a(35) and beyond from Andrew Howroyd, Jan 05 2018

Status

approved