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Search: id:A126326
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| A126326 |
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a(1) = 1; for n>1, a(n) = smallest number which is not a sum or product or power of any subset of the numbers a(1) to a(n-1). |
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+0
1
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| 1, 2, 5, 9, 13, 31, 35, 92, 118, 280, 516, 752, 1618, 1968, 5090, 6594, 15620, 19556, 48364, 61552
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Analogue of A065026, with powers.
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EXAMPLE
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a(4) = 9 because the possible sums and products of a(1), a(2), a(3) are 1, 2, 5, 1+2, 1+5, 2+5, 1+2+5, 2*5, 2^2, 2^3, ..., 5^2, 5^3, ... = 1, 2, 4, 3, 4, 5, 6, 7, 8, 10, 16, 25, ... The smallest missing number is 9.
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MAPLE
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A126326 := proc(amax) local a, n, sumset, prodset, j, powset, aprev, newsumset, newprodset ; a := [1, 2] ; n := 3 ; sumset := {} ; prodset := {1} ; powset := {1} ; while n <= amax do aprev := op(-1, a) ; newsumset := sumset ; for j from 1 to nops(sumset) do if op(j, sumset)+aprev <= amax then newsumset := newsumset union { op(j, sumset)+aprev } ; fi ; od ; for j from 1 to nops(a)-1 do if op(j, a)+aprev <= amax then newsumset := newsumset union { op(j, a)+aprev } ; fi ; od ; sumset := newsumset ; newprodset := prodset ; for j from 1 to nops(prodset) do if op(j, prodset)*aprev <= amax then newprodset := newprodset union { op(j, prodset)*aprev } ; fi ; od ; for j from 1 to nops(a)-1 do if op(j, a)*aprev <= amax then newprodset := newprodset union { op(j, a)*aprev } ; fi ; od ; prodset := newprodset ; for j from 2 to floor(log(amax)/log(aprev)) do if aprev^j <= amax then powset := powset union { aprev^j } ; fi ; od ; while n in sumset or n in prodset or n in powset do n := n+1 ; od ; if n <= amax then a := [op(a), n] ; fi ; print(a) ; n := n+1 ; od ; RETURN(a) ; end: A126326(200000) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 03 2007
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CROSSREFS
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Cf. A065026.
Sequence in context: A071705 A109094 A049753 this_sequence A070986 A074793 A161767
Adjacent sequences: A126323 A126324 A126325 this_sequence A126327 A126328 A126329
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KEYWORD
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easy,more,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 11 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 03 2007
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