

A052350


Smallest primes from A001359 where distance (A053319) to the next similar twin increases.


2



5, 17, 41, 617, 71, 311, 2267, 521, 1877, 461, 1721, 347, 1151, 1787, 3581, 2141, 6449, 1319, 21377, 1487, 12251, 4799, 881, 23057, 659, 19541, 12377, 2381, 38747, 10529, 37361, 8627, 9041, 33827, 5879, 80231, 15359, 45821, 36107, 14627, 37991
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Smallest distance (A052380) and also smallest possible increment of twindistances is 6.
Primes may occur between p+2 and p+6n.


LINKS

Table of n, a(n) for n=1..41.


FORMULA

The prime a(n) determines a prime quadruple: [p, p+2, p+6n, p+6n+2] and a [2, 6n2, 2] dpattern.


EXAMPLE

The first 3 terms (5,17,47) are followed by difference patterns as it is displayed: 5 by [2,4,2], 17 by [2,4+6,2], 41 by [2,4+6+6,2] determining prime quadruples: (5,7,11,13), (17,19,29,31) or (41,43,59,61) resp.
a(10)=461 gives the quadruple [461,463,521=461+60,523] and between 521 and 463 7 primes occur.


MATHEMATICA

NextLowerTwinPrim[n_] := Block[{k = n + 6}, While[ !PrimeQ[k]  !PrimeQ[k + 2], k += 6]; k]; p = 5; t = Table[0, {50}]; Do[ q = NextLowerTwinPrim[p]; d = (q  p)/6; If[d < 51 && t[[d]] == 0, t[[d]] = p; Print[{d, p}]]; p = q, {n, 1500}]; t (* Robert G. Wilson v, Oct 28 2005 *)


CROSSREFS

Cf. A001359, A053319, A007530, A052380, A052381, A113274, A113275.
Sequence in context: A106973 A102264 A122035 * A318826 A239195 A111746
Adjacent sequences: A052347 A052348 A052349 * A052351 A052352 A052353


KEYWORD

nonn


AUTHOR

Labos Elemer, Mar 07 2000


STATUS

approved



