The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A075058 Lexicographically earliest infinite sequence of distinct positive numbers with the property that every positive integer is a sum of distinct terms (see algorithm below). 7
 1, 2, 3, 7, 13, 23, 47, 97, 193, 383, 769, 1531, 3067, 6133, 12269, 24533, 49069, 98129, 196247, 392503, 785017, 1570007, 3140041, 6280067, 12560147, 25120289, 50240587, 100481167, 200962327, 401924639, 803849303, 1607698583, 3215397193, 6430794373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence starts with a(0)=1, subsequent terms a(n) for n > 0 being obtained by selecting the greatest prime <= 1 + Sum_{i=0..n-1} a(i). This ensures that the sequence has the required property because Sum_{i=0..n-1} a(i) >= a(n) - 1, for all n >= 0 and a(0)=1, is a necessary and sufficient condition for it to hold. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 0..1000 Wikipedia, "Complete" sequence. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - N. J. A. Sloane, May 20 2023] FORMULA a(n) = (greatest prime) <= 1 + Sum_{i=0..n-1} a(i). a(n) ~ k*2^n, with k roughly 0.748643. - Charles R Greathouse IV, Apr 05 2013 EXAMPLE Given that the first 7 terms of the sequence are 1,2,...,23,47 then a(8)=(greatest prime) <= (1+2+...+23,47) + 1 = 97, hence a(8)=97. MATHEMATICA prevprime[n_Integer] := (j=n; While[!PrimeQ[j], j--]; j) aprime[0]=1; aprime[n_Integer] := (aprime[n] = prevprime[Sum[aprime[m], {m, 0, n - 1}] + 1]); Table[aprime[p], {p, 0, 50}] a[0] = 1; a[n_] := a[n] = NextPrime[Sum[a[k], {k, 0, n-1}]+2, -1]; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Sep 30 2013 *) PROG (PARI) print1(s=1); for(n=1, 20, k=precprime(s+1); print1(", "k); s+=k) \\ Charles R Greathouse IV, Apr 05 2013 CROSSREFS Cf. A068524, A007924, A066352, A200947. Sequence in context: A091440 A175211 A330028 * A213968 A213967 A128695 Adjacent sequences: A075055 A075056 A075057 * A075059 A075060 A075061 KEYWORD nonn AUTHOR Amarnath Murthy, Sep 07 2002 EXTENSIONS Entry revised by Frank M Jackson, Dec 03 2011 Edited by N. J. A. Sloane, May 20 2023 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)