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A249114
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Take the counting numbers and continue adding 1, 2, ..., a(n) until one reaches a fourth prime.
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1
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7, 6, 19, 10, 12, 25, 11, 9, 40, 13, 15, 25, 11, 17, 67, 6, 15, 22, 15, 18, 43, 9, 12, 34, 12, 9, 31, 9, 32, 58, 8, 21, 28, 14, 12, 37, 11, 9, 55, 13, 23, 46, 11, 14, 43, 10, 15, 34, 24, 26, 28, 9, 15, 37, 23, 18, 40, 6, 24, 61, 8, 18, 43, 22, 27, 37, 20, 9
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OFFSET
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1,1
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COMMENTS
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It appears that the minimum value reached by a(n) is 6. This occurs for n=2, 16, 58, 136, 178, 418, 598, 808, ... . - Michel Marcus, Oct 26 2014
The conjecture in the previous line is true - if n is odd, then n+1 is even, n+3 is even, n+6 and n+10 are odd, etc., so a(n)>6. If n is even, then +1 and +3 are odd, +6, +10 are even, so the fourth prime can be first for a(n)=6. - Jon Perry, Oct 29 2014
Conjecture: a(n) is odd approximately 50% of the time. - Jon Perry, Oct 29 2014
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 7 because 1+1+2+3+4+5+6+7 = 29 and exactly three partial sums are prime (2,7,11).
a(2) = 6 because 2+1+2+3+4+5+6 = 23 and exactly three partial sums are prime (3,5,17).
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MAPLE
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f:= proc(n) local j, count;
count:= 0;
for j from 1 do
if isprime(n + j*(j+1)/2) then
count:= count+1;
if count = 4 then return j fi
fi
od
end proc:
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MATHEMATICA
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a[n_] := Module[{j, cnt = 0}, For[j = 1, True, j++, If[PrimeQ[n+j(j+1)/2], cnt++; If[cnt == 4, Return[j]]]]];
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PROG
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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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