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A287049 Prime p1 of consecutive primes p1, p2, where p2 - p1 = 8, and p1, p2 are in different centuries. 5
1193, 2699, 5399, 5693, 6599, 6899, 7499, 8093, 8699, 12899, 13799, 15299, 17099, 17393, 19793, 20399, 23993, 26099, 26399, 27893, 35099, 35393, 35999, 36299, 36599, 37493, 38699, 39293, 40499, 42299, 43793, 46499, 50093, 50993, 51599, 51899, 53093, 53993, 55799, 56393, 57593, 58199, 59399, 59699 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Since a(n) and a(n)+8 are consecutive primes either a(n)+7 or a(n)+1 is a multiple of 100; in addition a(n) must have the form 6k-1. Therefore, every century spanned by a(n) and a(n)+8 is a multiple of 300. It appears that every multiple of 3 occurs as the difference round((a(n+1)-a(n))/100); all multiples of 3 through 432 occur as these differences for a(n) < 1000000000.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

a287049[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[100, n, 100]], First[#]-Last[#]==8&]]

a287049[60000] (* data *)

Select[Partition[Prime[Range[6100]], 2, 1], #[[2]]-#[[1]]==8&&Floor[#[[1]]/ 100] != Floor[#[[2]]/100]&][[All, 1]] (* Harvey P. Dale, Oct 02 2019 *)

CROSSREFS

Cf. A001359, A158277, A160370, A160440, A160500.

Sequence in context: A040104 A103171 A032530 * A153379 A103172 A251923

Adjacent sequences:  A287046 A287047 A287048 * A287050 A287051 A287052

KEYWORD

nonn

AUTHOR

Hartmut F. W. Hoft, May 18 2017

STATUS

approved

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)