A196938 a(n) is the prime number that is the center element (3rd) of a 5-terms arithmetic progression prime chain.

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

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 5-term 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 5-term 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