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Search: id:A127596
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| A127596 |
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Numbers n such that 1 + Sum{k=1..n-1} A001223(k)*(-1)^k = 0. |
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4
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| 2, 4, 14, 22, 28, 233, 249, 261, 488, 497, 511, 515, 519, 526, 531, 534, 548, 562, 620, 633, 635, 2985, 3119, 3123, 3128, 3157, 4350, 4358, 4392, 4438, 4474, 4484, 4606, 4610, 4759, 5191, 12493, 1761067, 2785124, 2785152, 2785718, 2785729, 2867471
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Or, with prime(0) = 1, numbers n such that Sum{k=0..n-1} (prime(k+1)-prime(k))*(-1)^k = Sum{k=0..n-1} (A008578(k+1)-A008578(k))*(-1)^k = 0.
Sequence has 313 terms < 10^7, 846 terms < 10^8.
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LINKS
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K. Brockhaus, Table of n, a(n) for n=1..846
Eric Weisstein's World of Mathematics, Andrica's Conjecture
Eric Weisstein's World of Mathematics, Prime Difference Function
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EXAMPLE
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1 - A001223(1) = 1-1 = 0, hence 2 is a term.
1 - A001223(1) + A001223(2) - A001223(3) = 1-1+2-2 = 0, hence 4 is a term.
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MAPLE
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S=0; Do[j=Prime[n+1]; i=Prime[n]; d[n]=j-i; S=S+(d[n]*(-1)^n); If[S+1==0, Print[Table[j|PrimePi[j]|S+1]]], {n, 1, 10^7, 1}]
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PROGRAM
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(PARI) {m=10^8; n=1; p=1; e=1; s=0; while(n<m, q=nextprime(p+1); s=s+(q-p)*e; if(s==0, print1(n, ", ")); p=q; e=-e; n++)} /* Klaus Brockhaus, Apr 29 2007 */
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CROSSREFS
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Cf. A001223 (differences between consecutive primes), A008578 (prime numbers at the beginning of the 20th century), A000101 (increasing gaps between primes, upper end), A002386 (increasing gaps between primes, lower end).
Adjacent sequences: A127593 A127594 A127595 this_sequence A127597 A127598 A127599
Sequence in context: A032309 A008519 A071865 this_sequence A111871 A090808 A074716
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KEYWORD
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nonn
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AUTHOR
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Manuel Valdivia (mvaldivia(AT)ugr.es), Apr 03 2007
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EXTENSIONS
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Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 29 2007
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