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Search: id:A064934
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| A064934 |
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Smallest prime (or non-composite) strictly greater than sum of previous terms [with a(0)=1]. |
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+0
10
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| 1, 2, 5, 11, 23, 43, 89, 179, 359, 719, 1433, 2879, 5749, 11497, 22993, 45989, 91997, 183971, 367949, 735901, 1471807, 2943599, 5887213, 11774429, 23548853, 47097697, 94195421, 188390809, 376781623, 753563269, 1507126519, 3014253049
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Seems to tend towards 2^(n+0.4891533...); replacing "prime" by "number" or "power of 2" and starting with a(0)=1, it would be 2^n; with primes starting with a(1)=2 but no a(0), it seems as if it could tend towards 2^(n-0.07323...); while with squares starting with a(0)=0 it seems as if it would tend towards 2^(n+0.4294...); it seems plausible that all such sequences have similar properties providing that the underlying sequence is increasing but no faster than 2^n.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,200
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MATHEMATICA
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NextPrim[n_Integer] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = {1}; Do[a = Append[a, NextPrim[ Apply[ Plus, a]]], {n, 1, 32} ]; a
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PROGRAM
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(PARI) { for (n=0, 200, if (n, a=nextprime(s + 1); s+=a, a=s=1); write("b064934.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 29 2009]
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CROSSREFS
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Sequence in context: A039693 A062475 A124920 this_sequence A005986 A147878 A140992
Adjacent sequences: A064931 A064932 A064933 this_sequence A064935 A064936 A064937
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Oct 26 2001
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