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Search: id:A054892
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| A054892 |
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Smallest prime a(n) such that the sum of n consecutive primes starting with a(n) is divisible by n. |
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+0
4
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| 2, 3, 3, 5, 71, 5, 7, 17, 239, 13, 29, 5, 43, 23, 5, 5, 7, 7, 79, 17, 47, 11, 2, 73, 97, 53, 271, 13, 263, 23, 41, 61, 97, 101, 181, 41, 47, 13, 233, 13, 53, 13, 359, 151, 71, 61, 239, 73, 443, 859, 29, 131, 2, 61, 313, 101, 19, 151, 521, 3, 571, 31, 7, 79, 109, 97, 53
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In accidental cases (n=1,2,25,..), like a(25)=97, the sum of 25 consecutive primes starts with the 25th prime and is divided by 25: Sum=97+...+227=3925=25*157
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FORMULA
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Min[q_1; Sum[q_i; {i, 1, n}]]=n*X], q_i is a prime (rarely only q_i=Prime[i])
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EXAMPLE
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n=1: a(1)=2 and 2 is divisible by 1.
n=3: a(3)=3 and 3+5+7=15=3*5.
n=8: a(8)=17 and 17+19+23+29+31+37+41+43=240=8*30
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MATHEMATICA
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f[n_] := Block[{k = 1, t}, While[t = Table[Prime[i], {i, k, k + n - 1}]; Mod[Plus @@ t, n] > 0, k++ ]; t]; First /@ Table[f[n], {n, 67}] (*Chandler*)
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CROSSREFS
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Cf. A054643, A024672, A034961, A077388, A077389, A122820.
Sequence in context: A064776 A096659 A046826 this_sequence A104570 A071915 A021432
Adjacent sequences: A054889 A054890 A054891 this_sequence A054893 A054894 A054895
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 23 2000
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