cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A160370 Smaller member p of a pair (p,p+6) of consecutive primes in different centuries.

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%I A160370 #14 May 20 2017 22:49:53
%S A160370 1097,2897,3797,4597,5297,5897,9397,11497,11897,12197,12497,12697,
%T A160370 15797,16097,18797,19597,21997,24097,24197,28597,28697,29297,30097,
%U A160370 30197,30697,32497,35597,36997,39097,40897,41597,41897,42397,45497,47297
%N A160370 Smaller member p of a pair (p,p+6) of consecutive primes in different centuries.
%C A160370 Note that the smaller member of a pair of sexy primes with the same constraint on centuries defines a different sequence, since members of a sexy prime pair do not need to be *consecutive* primes.
%C A160370 The larger member in the pair is obtained by adding 6 to an entry.
%C A160370 Every a(n)+3 is a multiple of 100 such that neither a(n)+2 nor a(n)+4 are primes. It appears that every integer occurs as the difference round((a(n+1)-a(n))/100); all numbers 1..333 occur as these differences for a(n) < 1000000000. - _Hartmut F. W. Hoft_, May 18 2017
%H A160370 Harvey P. Dale, <a href="/A160370/b160370.txt">Table of n, a(n) for n = 1..2000</a>
%F A160370 {A031924(n): [A031924(n)/100] <> [A031925(n)/100]} where [..]=floor(..).
%e A160370 30097 + 6 = 30103.
%t A160370 Transpose[Select[Partition[Prime[Range[5000]],2,1],#[[2]]-#[[1]] == 6 && Floor[#[[1]]/100]!=Floor[#[[2]]/100]&]][[1]] (* _Harvey P. Dale_, Apr 28 2012 *)
%t A160370 a160370[n_] := Select[Range[97, n, 100], AllTrue[# + {0, 6}, PrimeQ] && NoneTrue[# + {2, 4}, PrimeQ]&]
%t A160370 a160370[49000] (* data *) (* _Hartmut F. W. Hoft_, May 18 2017 *)
%Y A160370 Cf. A158277, A046117, A023201.
%K A160370 nonn
%O A160370 1,1
%A A160370 _Ki Punches_, May 11 2009
%E A160370 Edited by _R. J. Mathar_, May 14 2009