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A249112
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Second smallest k > 0 such that n+(1+2+...+k) is prime.
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3
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3, 2, 7, 2, 8, 10, 4, 5, 7, 2, 8, 10, 4, 5, 16, 2, 8, 10, 7, 6, 16, 5, 8, 22, 7, 5, 16, 2, 15, 22, 4, 6, 7, 9, 8, 13, 4, 5, 19, 2, 11, 10, 7, 5, 16, 5, 8, 13, 12, 6, 7, 5, 8, 22, 7, 5, 16, 2, 15, 13, 4, 9, 16, 5, 8, 13, 8, 5, 7, 2, 11, 10, 4, 14, 16, 6, 8
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OFFSET
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1,1
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COMMENTS
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Take the counting numbers and continue adding 1, 2, ..., a(n) until reaching a second prime.
It appears that the minimum value reached by a(n) is 2, and this occurs for n= 2, 4, 10, 16, 28, 40, 58, 70, ... Is this A144834? - Michel Marcus, Oct 26 2014
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LINKS
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FORMULA
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n+A000217(k) is prime for k=a(n) and exactly one smaller positive value. - M. F. Hasler, Oct 21 2014
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EXAMPLE
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a(3)=7 because 3+1+2+3+4+5+6+7=31 and one partial sum is prime.
a(4)=2 because 4+1=5 and 4+1+2=7.
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MATHEMATICA
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Table[k = 0; Do[k++; While[! PrimeQ[n + Total@ Range@ k], k++], {x, 2}]; k, {n, 77}] (* Michael De Vlieger, Jan 03 2016 *)
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PROG
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(PARI) a(n, s=2)=my(k); until(isprime(n+=k++)&&!s--, ); k \\ allows one to get A249113(n) as a(n, 3). - M. F. Hasler, Oct 21 2014
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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