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A086424
Numbers needed to generate all other natural numbers, only allowing multiplication and addition. Each number can be used only once.
0
1, 2, 4, 11, 25, 64, 171, 569, 3406, 27697, 243374, 1759619, 28381401, 222323189, 3416307938, 26838745347
OFFSET
1,2
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
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