|
A079016
|
|
Suppose p and q = p+12 are primes. Define the difference pattern of (p,q) to be the successive differences of the primes in the range p to q. There are 14 possible difference patterns, namely [12], [2,10], [4,8], [6,6], [8,4], [10,2], [2,4,6], [2,6,4], [4,2,6], [4,6,2], [6,2,4], [6,4,2], [2,4,2,4] and [4,2,4,2]. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.
|
|
6
|
|
|
%I #7 Feb 26 2017 02:27:58
%S 5,7,17,19,29,31,47,67,89,137,139,199,397,1601
%N Suppose p and q = p+12 are primes. Define the difference pattern of (p,q) to be the successive differences of the primes in the range p to q. There are 14 possible difference patterns, namely [12], [2,10], [4,8], [6,6], [8,4], [10,2], [2,4,6], [2,6,4], [4,2,6], [4,6,2], [6,2,4], [6,4,2], [2,4,2,4] and [4,2,4,2]. Sequence gives smallest value of p for each difference pattern, sorted by magnitude.
%e p=1601, q=1613 has difference pattern [6,2,4] and {1601,1607,1609,1613} is the corresponding consecutive prime 4-tuple.
%t Function[s, Function[t, Union@ Flatten@ Map[s[[First@ Position[t, #]]] &, {{12}, {2, 10}, {4, 8}, {6, 6}, {8, 4}, {10, 2}, {2, 4, 6}, {2, 6, 4}, {4, 2, 6}, {4, 6, 2}, {6, 2, 4}, {6, 4, 2}, {2, 4, 2, 4}, {4, 2, 4, 2}}]]@ Map[Differences@ Select[Range[#, # + 12], PrimeQ] &, s]]@ Select[Prime@ Range[10^3], PrimeQ[# + 12] &] (* _Michael De Vlieger_, Feb 25 2017 *)
%Y A022006(1)=5, A022007(1)=7, A078847(1)=17, A078851(1)=19, A078848(1)=29, A078855(1)=31, A047948(1)=47, A078850(1)=67, A031930(1)=A000230(6)=199, A046137(1)=7, A078853(1)=1601.
%Y Cf. A079017-A079024.
%K fini,full,nonn
%O 1,1
%A _Labos Elemer_, Jan 24 2003
|
