A052350 Smallest primes from A001359 where the distance (A053319) to the next similar twin increases.

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

Offset

1,1

Comments

Smallest distance (A052380) and also smallest possible increment of twin-distances is 6.

Primes may occur between p+2 and p+6n.

Links

Norman Luhn, Table of n, a(n) for n = 1..4624 (terms 1..4500 from Martin Raab).

Formula

The prime a(n) determines a prime quadruple: [p, p+2, p+6n, p+6n+2] and a [2, 6n-2, 2] d-pattern.

Example

The first 3 terms (5, 17, 41) 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), respectively.
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