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A202618 a(n) is the smallest integer that is the sum of n distinct members of the complete sequence A075058. 0
0, 1, 4, 6, 19, 42, 89, 96, 289, 672, 1441, 2972, 6039, 12172, 24441, 48974, 98043, 196172, 392419, 784922, 1569939, 3139946, 6279987, 12560054, 25120201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Any nonnegative integer can be written as a sum of distinct members of A075058 because it is a complete sequence. a(n) is the smallest integer that is the sum of n distinct members of A075058 in the same way that A066352 gives a Pillai sequence for the complete sequence comprising 1 followed by all the primes.

LINKS

Table of n, a(n) for n=0..24.

Wikipedia, Complete sequence.

FORMULA

Find smallest m such that Binary(A201997(m)) x {1,1,1.....} = n, where x is the inner product, {1,1,1,1,...} is an infinite binary vector of 1's and Binary(A201997(m)) a binary vector with infinite trailing zeros both in ascending powers of 2. Then a(n) = Binary(m) x A075058, where x is the inner product and the binary vector is in ascending powers of 2 with infinite trailing zeros.

EXAMPLE

For n=5, the binary vector at A201997(54) is the smallest binary vector containing 5, 1's and when applied to A075058 selects the integer 42. Consequently because 42=23+13+3+2+1 and 1,2,3,13,23 are all members of the complete sequence A075058, then a(5)=42.

MATHEMATICA

prevprime[n_Integer] := (j=n; If[n==1, 1, While[!PrimeQ[j], j--]; j]); aprime[n_Integer] := (aprime[n]=prevprime[Sum[aprime[m], {m, 0, n - 1}]+1]); gentable[n_Integer] := (m=n; ptable={0}; While[m!=0, (i=0; While[aprime[i]<=m && ptable[[i+1]]!=1, (AppendTo[ptable, 0]; i++)]; ptable[[i]] = 1; m=m-aprime[i - 1])]; ptable); decimal[n_Integer] := (gentable[n]; Sum[2^(k-1)*ptable[[k]], {k, 1, Length[ptable]}]); ones[n_Integer] :=(gentable[n]; Sum[ptable[[k]], {k, 1, Length[ptable]}]); changeones[n_Integer] := (p = 0; While[ones[p] < n, p++]; p); aprime[0]=1; Table[changeones[r], {r, 0, 20}]

CROSSREFS

Cf. A007924, A066352, A200947, A075058, A201997

Sequence in context: A116383 A026521 A222379 * A006534 A064035 A010364

Adjacent sequences:  A202615 A202616 A202617 * A202619 A202620 A202621

KEYWORD

nonn,more

AUTHOR

Frank M Jackson, Dec 21 2011

STATUS

approved

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Last modified November 18 17:33 EST 2019. Contains 329287 sequences. (Running on oeis4.)