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A047160 a(2) = a(3) = 0; for n >= 4, a(n) = smallest number m such that n-m and n+m are both primes, or -1 if no such m exists. +0
3
0, 0, 1, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 9, 0, 5, 6, 3, 4, 9, 0, 1, 0, 9, 4, 3, 6, 5, 0, 9, 2, 3, 0, 1, 0, 3, 2, 15, 0, 5, 12, 3, 8, 9, 0, 7, 12, 3, 4, 15, 0, 1, 0, 9, 4, 3, 6, 5, 0, 15, 2, 3, 0, 1, 0, 15, 4, 3, 6, 5, 0, 9, 2, 15, 0, 5, 12, 3, 14, 9, 0, 7, 12, 9, 4, 15, 6, 7, 0, 9, 2, 3 (list; graph; listen)
OFFSET

2,7

COMMENT

The even terms of this sequence are of interest for the Goldbach conjecture. - T. D. Noe (noe(AT)sspectra.com), Aug 01 2002

I have confirmed there are no -1 entries through integers to 4.29*10^9 using Pari. - Bill McEachen (bmceache(AT)centralsan.dst.ca.us), Jul 07 2008

LINKS

T. D. Noe, Table of n, a(n) for n=2..10000

EXAMPLE

16-3=13 and 16+3=19 are primes, so a(16)=3.

MATHEMATICA

For[lst={}; n=2, n<=100, n++, If[EvenQ[n]&&n>2, del=1, del=0]; While[del<n&&!(PrimeQ[n-del]&& PrimeQ[n+del]), del=del+2]; If[del==n, del=-1]; AppendTo[lst, del]]; lst

PROGRAM

(UBASIC) 10 N=2// 20 M=0// 30 if and{prmdiv(N-M)=N-M, prmdiv(N+M)=N+M} then print M; :goto 50// 40 inc M:goto 30// 50 inc N: if N>130 then stop// 60 goto 20

CROSSREFS

Cf. A002372, A035026.

Sequence in context: A053370 A016458 A058513 this_sequence A093347 A134676 A103491

Adjacent sequences: A047157 A047158 A047159 this_sequence A047161 A047162 A047163

KEYWORD

nonn,easy,nice

AUTHOR

Lior Manor (lior.manor(AT)gmail.com)

EXTENSIONS

More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), May 15 1999.

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Last modified September 7 23:08 EDT 2008. Contains 143486 sequences.


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