A086424 Numbers needed to generate all other natural numbers, only allowing multiplication and addition. Each number can be used only once.

1, 2, 4, 11, 25, 64, 171, 569, 3406, 27697, 243374, 1759619, 28381401, 222323189, 3416307938, 26838745347

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Formula

a(n) >= 2a(n-1). - Charles R Greathouse IV, Jun 17 2013

Example

10 is not in the sequence because (4+1)*2 = 10.
11 is in the sequence because there is no way to get 11 by using the earlier terms.
509 is not in the sequence because 509 = (1+25)*(2+11)+171.

Prog

(PARI) Ww(v)=if(#v==2, return([v[1], v[2], v[1]+v[2], v[1]*v[2]])); my(V=[], t); for(i=1, #v-1, for(j=i+1, #v, t=vecextract(v, 2^#v-1-2^(i-1)-2^(j-1)); V=concat(V, concat(Ww(concat(t, v[i]+v[j])), Ww(concat(t, v[i]*v[j]))))); V=vecsort(V, , 8)); V
a=[1, 2, 4]; for(n=3, 9, V=Ww(a); for(i=2*a[#a], #V, if(V[i]>i, print(a=concat(a, i)); break))) \\ Charles R Greathouse IV, Jun 17 2013

Crossrefs

Sequence in context: A100550 A329707 A071973 * A122121 A368412 A080009

Adjacent sequences: A086421 A086422 A086423 * A086425 A086426 A086427

Keyword

more,nonn,nice

Author

Arno Bouwes (acbouwes(AT)hotmail.com), Sep 08 2003

Extensions

Corrected and extended by Don Reble, Sep 21 2003

Two more terms from Jon E. Schoenfield, Aug 24 2009

a(13)-a(15) from Giovanni Resta, Jun 22 2013

a(16) from Bert Dobbelaere, Apr 03 2024

Status

approved