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A129758
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Smallest prime p such that there are primes q and r with the property that p, q and r form an arithmetic progression and their sum is the same as three times the (n+2)-nd prime number.
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1
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3, 3, 5, 7, 11, 7, 17, 17, 19, 31, 29, 19, 41, 47, 47, 43, 61, 59, 67, 61, 59, 71, 67, 89, 97, 101, 79, 89, 103, 113, 107, 127, 131, 139, 151, 127, 137, 167, 167, 163, 149, 163, 167, 157, 199, 163, 197, 181, 227, 227, 211, 239, 251, 257, 257, 229, 271, 269
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The same selection rule as in A078497 applies: if there is more than one prime triple (p,q=p+d,r=q+d) with p+q+r=A001748(n), take p from the triple with minimum d. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2007
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FORMULA
| A078497(n)-prime(n)=prime(n)-a(n)=d. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2007
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EXAMPLE
| 3 + 5 + 7 = 15, which is three times the (1+2)th prime number. Thus a(1) = 3.
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MAPLE
| A129758 := proc(n) local p3, i, d, r, p; p3 := ithprime(n) ; i := n+1 ; while true do r := ithprime(i) ; d := r-p3 ; p := p3-d ; if isprime(p) then RETURN(p) ; fi ; i := i+1 ; od ; RETURN(-1) ; end: for n from 3 to 60 do printf("%d, ", A129758(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 19 2007
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MATHEMATICA
| a[n_]:=Module[{}, k=1; While[Not[PrimeQ[Prime[n+1]-k] && PrimeQ[Prime[n+1]+k]], k++ ]; Prime[n + 1] - k]; Table[a[n], {n, 2, 60}]
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CROSSREFS
| Cf. A078497, A071681, A078611.
Sequence in context: A086341 A176513 A128424 * A176347 A161834 A141867
Adjacent sequences: A129755 A129756 A129757 * A129759 A129760 A129761
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KEYWORD
| easy,nonn
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AUTHOR
| Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), May 15 2007
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EXTENSIONS
| Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 19 2007
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