A078497 The member r of a triple of primes (p,q,r) in arithmetic progression which sum to 3*prime(n) = A001748(n) = p + q + r.

7, 11, 17, 19, 23, 31, 29, 41, 43, 43, 53, 67, 53, 59, 71, 79, 73, 83, 79, 97, 107, 107, 127, 113, 109, 113, 139, 137, 151, 149, 167, 151, 167, 163, 163, 199, 197, 179, 191, 199, 233, 223, 227, 241, 223, 283, 257, 277, 239, 251, 271, 263, 263, 269, 281, 313

Offset

3,1

Comments

In case more than one triple of primes p, q=p+d and r=p+2*d exists, we take r=a(n) from the triple with the smallest d. This shows the difference from A092940, which would take the maximum r over all triples. - R. J. Mathar, May 19 2007

Links

Table of n, a(n) for n=3..58.

Example

a(1) = 7 because 3+5+7 = 15;
a(2) = 11 because 3+7+11 = 21;
a(3) = 17 because 5+11+17= 33.

Maple

A078497 := 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(r) ; fi ; i := i+1 ; od ; RETURN(-1) ; end: for n from 3 to 60 do printf("%d, ", A078497(n)) ; od ; # R. J. Mathar, May 19 2007

Mathematica

f[n_] := Block[{p = Prime[n], k}, k = p + 1; While[ !PrimeQ[k] || !PrimeQ[2p - k], k++ ]; k]; Table[ f[n], {n, 3, 60}]

Crossrefs

Cf. A078496, A078498, A001748, A092940, A071681, A078611.

Sequence in context: A038880 A019365 A191055 * A274505 A256567 A155048

Adjacent sequences: A078494 A078495 A078496 * A078498 A078499 A078500

Keyword

nonn

Author

Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), Nov 27 2002

Extensions

Edited and extended by Robert G. Wilson v, Nov 29 2002

Further edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar

Status

approved