The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A168556 Smallest primes p = p(k) with (p(k)+p(k+1)+p(k+2))/15 an integer. 0
 3, 4691, 6397, 6911, 8893, 10181, 11833, 12113, 13063, 13267, 14251, 16661, 17851, 20563, 21341, 21881, 22229, 22877, 23339, 23633, 24859, 26561, 26591, 27337, 27361, 28151, 29531, 30029, 30211, 30881, 30983, 31271, 33961, 34439, 35227 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS (1) Denominator 15 = p(2)+ p(3)+ p(4) is sum of the first 3 consecutive odd primes. (2) First three consecutive odd primes 3, 5, 7 are an exceptional case, because of p(k+1)=p(3)=5, no other prime has end digit 5. (3) Four out of 19 possibilities for end digit permutations (which all "happen") of three consecutive primes p(k), p(k+1) and p(k+2) are permutations of (1,1,3), (1,7,7), (3,3,9) and (7,9,9), as sum of these digits has to be necessarily a multiple of 5. (4) Note the "gap" for a(1) and a(2). REFERENCES Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005 Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005 LINKS EXAMPLE (1) 3 + 5 + 7 = 15 * 1 => a(1)=3 for k=2. (2) 4691 + 4703 + 4721 = 14115 = 15 * 941 => a(2)=4691 for k=634. (3) 6397 + 6421 + 6427 = 19245 = 15 * 1283 => a(3)=6397 for k=834. (4) 8893 + 8923 + 8929 = 26745 = 15 * 1783 => a(5)=8893 for k=1108. (5) 23339 + 23357 + 23369 = 70065 = 15 * 4671 => a(19)=23339 for k=2603. PROG (PARI) lista(nn) = {vp = primes(nn); for (k = 1, nn - 2, if ((vp[k] + vp[k+1] + vp[k+2]) % 15 == 0, print1(vp[k], ", ")); ); } \\ Michel Marcus, Aug 27 2013 CROSSREFS Cf. A000040 The prime numbers Cf. A168069 a(n) is the index k of the smallest prime p(k) with (p(k) + p(k+1))/n an integer Sequence in context: A229766 A003166 A251603 * A200950 A307210 A171362 Adjacent sequences:  A168553 A168554 A168555 * A168557 A168558 A168559 KEYWORD nonn AUTHOR Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 29 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)