A129918 Smallest prime of the form k*prime(n+1)+prime(n) = j*prime(n+2)+prime(n+1) for free integer multipliers k and j.

23, 103, 271, 271, 557, 3209, 2411, 6229, 2633, 401, 2251, 28163, 19219, 13297, 3121, 46663, 17749, 2339, 41389, 25037, 121259, 261031, 6491, 19489, 41507, 192917, 163171, 6211, 4177, 440549, 59863, 247279, 120233, 21893, 102829, 435041, 13523

Offset

1,1

Comments

A prime (like 271) occurring more than once ought be rare. It requires four primes to be linked by two congruences. The sequence of the 2nd smallest primes of the form is 53, 173, 733, 557, 2767, 5147, 4159, 12899, 6229, ... The list of 3rd smallest primes is 83, 313, 887, 1129, 3209, 8377, 6781, 16901, ... - R. J. Mathar, Sep 02 2007

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

For n = 3, prime(3,4,5) = (5,7,11), we have 38*7+5 = 24*11+7 = 271, a prime, with (k,j) = (38,24).

Maple

A129918 := proc(n) local p, q, r, m ; p := ithprime(n) ; q := nextprime(p) ; r := nextprime(q) ; m := chrem([p, q], [q, r]) ; while not isprime(m) do m := m+ r*q ; od ; RETURN(m) ; end: seq(A129918(n), n=1..40) ; # R. J. Mathar, Sep 02 2007

Crossrefs

Somewhat related to A072999.

Sequence in context: A139976 A241746 A142192 * A240839 A138715 A096324

Adjacent sequences: A129915 A129916 A129917 * A129919 A129920 A129921

Keyword

nonn

Author

J. M. Bergot, Jun 05 2007

Extensions

Edited by R. J. Mathar, Sep 02 2007

Status

approved