A084299 Smallest primes such that the subsequent terms of consecutive prime differences[A001223] modulo 6 [A054763] displays repeatedly n times a {0,2,4} pattern of remainders of differences.

83, 2903, 5897, 319499, 346943, 7974179, 15262433, 33954251

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Example

n=1: a(1)=83 is followed by [6,8,4],
n=2: a(2)=2903 is followed by [6,2,4,18,2,4]
n=3: a(3)=5897 is followed by [6,20,4,12,14,28,6,20,4]
n=4: a(4)=319499 is followed by [12,8,22,6,20,10,12,2,10,6,32,34]
n=5: a(5)=346943 is followed by [18,2,40,....,30,2,10] differences corresponding to n "wavelet" of [0,2,4] remainders modulo 6.

Mathematica

d[x_] := Prime[x+1]-Prime[x] md[x_] := Mod[Prime[x+1]-Prime[x], 6] h={k1=0, k2=2, k3=4}; k=0; Do[If[Equal[md[n], k1]&&Equal[md[n+1], k2]&& Equal[md[n+2], k3]&&Equal[md[n+3], k1]&&Equal[md[n+4], k2]&&Equal[md[n+5], k3] &&Equal[md[n+6], k1]&&Equal[md[n+7], k2]&&Equal[md[n+8], k3] &&Equal[md[n+9], k1]&&Equal[md[n+10], k2]&&Equal[md[n+11], k3]&& Equal[md[n+12], k1]&&Equal[md[n+13], k2]&&Equal[md[n+14], k3], k=k+1; Print[{de, k, n, Prime[n], Table[md[n+j], {j, -1, 15}], Table[d[n+j], {j, -1, 15}]}]], {n, 2, 10000000}]

Crossrefs

Cf. A001223, A054763, A016045.

Sequence in context: A093283 A332615 A156924 * A017799 A017746 A220649

Adjacent sequences: A084296 A084297 A084298 * A084300 A084301 A084302

Keyword

more,nonn

Author

Labos Elemer, Jun 02 2003

Status

approved