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Search: id:A084834
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| A084834 |
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a(n) is the smallest number not previously used such that a(n)+a(n-1), a(n)+a(n-1)+a(n-2), ..., a(n)+...+a(1) are not prime. |
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2
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| 1, 3, 5, 7, 9, 11, 13, 15, 17, 4, 6, 30, 38, 10, 36, 14, 34, 42, 39, 21, 69, 27, 33, 45, 20, 16, 24, 50, 25, 51, 66, 18, 72, 54, 60, 74, 22, 8, 19, 41, 28, 48, 44, 40, 78, 57, 35, 58, 102, 12, 63, 65, 64, 56, 46, 96, 68, 76, 114, 80, 52, 84, 90, 99, 55, 2, 93, 75, 100, 62, 120, 98
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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No sum of a continuous subsequence is ever prime. Is every integer used? Can an odd number ever be surrounded by two even numbers (and similarly for even numbers)?
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EXAMPLE
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a(4)=7 because 7 is the smallest unused number such that 1+3+5+x, 3+5+x and 5+x are all composite
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PROGRAM
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(PARI) { checkprime(a, b)=local(fl); fl=0; for (i=1, b-1, if (isprime(a+s[i]), fl=1; break)); if (fl==0, for (j=1, b-1, if (a==p[j], fl=1; break))); fl } { p=vector(300); p[1]=1; pc=2; while (pc<300, x=1; s=vector(300); for (i=1, pc-1, s[i]=sum(k=i, pc-1, p[k])); i=1; while (checkprime(x, pc), x++); p[pc]=x; pc++); p }
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CROSSREFS
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Cf. A084834.
Sequence in context: A134322 A063460 A024806 this_sequence A118137 A063280 A094042
Adjacent sequences: A084831 A084832 A084833 this_sequence A084835 A084836 A084837
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jun 06 2003
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