

A129758


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.


1



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
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OFFSET

1,1


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, May 19 2007


LINKS

Table of n, a(n) for n=1..58.


FORMULA

A078497(n)prime(n)=prime(n)a(n)=d.  R. J. Mathar, May 19 2007


EXAMPLE

3 + 5 + 7 = 15, which is three times the (1+2)th prime number. Thus a(1) = 3.


MAPLE

A129758 := proc(n) local p3, i, d, r, p; p3 := ithprime(n) ; i := n+1 ; while true do r := ithprime(i) ; d := rp3 ; p := p3d ; 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, May 19 2007


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}]


CROSSREFS

Cf. A078497, A071681, A078611.
Sequence in context: A086341 A176513 A128424 * A176347 A161834 A141867
Adjacent sequences: A129755 A129756 A129757 * A129759 A129760 A129761


KEYWORD

easy,nonn


AUTHOR

Giovanni Teofilatto, May 15 2007


EXTENSIONS

Edited and extended by R. J. Mathar, Giovanni Teofilatto and Stefan Steinerberger, May 19 2007


STATUS

approved



