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Search: id:A143851
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| A143851 |
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Primes that divide the sum of their residues modulo all smaller primes |
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+0
2
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OFFSET
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1,1
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COMMENT
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No other terms below 10^7. [From Max Alekseyev (maxale(AT)gmail.com), Sep 13 2009]
10^8 < a(6) <= 724031017. a(7) <= 1990127567. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 25 2009]
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FORMULA
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Primes p such that p divides A034387([p/1]) + A034387([p/2]) + ... + A034387([p/p]) = A034387([p/1]) + ... + A034387([p/m]) - m*A034387(m) + \sum_{prime q<=m} q*[p/q], where m = [sqrt(p)]. [From Max Alekseyev (maxale(AT)gmail.com), Sep 13 2009]
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EXAMPLE
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13 is congruent to 1,1,3,6 and 2, mod 2,3,5,7 and 11 respectively. 1+1+3+6+2=13, which is a multiple of the original number, 13. So the original number, is in the sequence.
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MATHEMATICA
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For[n = 1, n < 1000001, n++, p = Prime[n]; m = Mod[Sum[Mod[p, Prime[i]], {i, 1, n - 1}], p]; If[m == 0, Print[p]]]
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CROSSREFS
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Cf. A065132
Sequence in context: A090643 A132521 A078363 this_sequence A088316 A006905 A119400
Adjacent sequences: A143848 A143849 A143850 this_sequence A143852 A143853 A143854
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KEYWORD
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more,nonn,new
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AUTHOR
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N. Fernandez (ncf(AT)borve.org), Sep 03 2008
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