

A196938


a(n) is the prime number that is the center element (3rd) of a 5terms arithmetic progression prime chain.


2



17, 29, 67, 71, 89, 97, 101, 131, 163, 167, 173, 191, 193, 197, 211, 233, 241, 257, 263, 269, 283, 307, 313, 317, 337, 347, 373, 419, 433, 443, 449, 457, 461, 463, 467, 479, 491, 503, 509, 521, 523, 547, 577, 599, 601, 607, 617, 619, 631, 641, 643, 677, 683
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OFFSET

1,1


COMMENTS

The Mathematica program gives the first 53 terms.
The Mathematica program is also good for finding sequences with any odd number of terms.


LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000


EXAMPLE

{5,13,[17],23,29} is a 5term arithmetic progression prime chain, so a(1)=17; (for all primes smaller than 17, no such chains exist)
{5,17,[29].41,53} is a 5term arithmetic progression prime chain, so a(2)=29; (for all primes in between 17 and 29, no such chains exist)


MATHEMATICA

terms = 5; max=53; i = 1; step = (terms  1)/2; Table[While[i++; p = Prime[i]; found = 0; j = 0; While[j++; df = 6*j; (p > (step*df)) && (found == 0), found = 1; Do[If[(! PrimeQ[p  k*df])  (! PrimeQ[p + k*df]), found = 0], {k, 1, step}]]; found == 0]; p, {ct, 1, max}]


CROSSREFS

Cf. A033451.
Sequence in context: A089629 A007349 A154616 * A225943 A069755 A076727
Adjacent sequences: A196935 A196936 A196937 * A196939 A196940 A196941


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Oct 07 2011


STATUS

approved



