%I #14 Sep 19 2018 15:00:28
%S 541,547,557,1019,4229,4231,35099,59617,91199,105997,708251,998969,
%T 1208209,1260323,1376461,1435997,1556393,1752197,1996217,2092249,
%U 2152811,2271383,2349917,3011011,3919199,3919211,4020167,4020197,4089037,4089073,4797503,4897331,5124023
%N Initial member of 10 consecutive primes {a, b, c, d, e, f, g, h, i, j} such that (j - e) = (i - d) = (h - c) = (g - b) = (f - a).
%C 12689273 is the smallest term such that 12689273 +- 6 are both prime.
%H Harvey P. Dale, <a href="/A293393/b293393.txt">Table of n, a(n) for n = 1..100</a>
%e 541 is a term because it is the initial member of 10 consecutive primes {541, 547, 557, 563, 569, 571, 577, 587, 593, 599} = {a, b, c, d, e, f, g, h, i, j}: {(j - e) = (i - d) = (h - c) = (g - b) = (f - a)} = {(599 - 569) = (593 - 563) = (587 - 557) = (577 - 547) = (571 - 541)} = 30.
%p A293393:= proc(n)local a, b, c, d, e, f, g, h, i, j; a:=ithprime(n); b:=ithprime(n+1); c:=ithprime(n+2); d:=ithprime(n+3); e:=ithprime(n+4); f:=ithprime(n+5); g:=ithprime(n+6); h:=ithprime(n+7); i:=ithprime(n+8); j:=ithprime(n+9); if (j - e) = (i - d) and (j - e)= (h - c) and (j - e)= (g - b) and (j - e)= (f - a)then RETURN (a); fi; end: seq(A293393(n), n=1..500000);
%p # Alternative:
%p P:= select(isprime, [seq(i,i=3..10^7,2)]):
%p Q:= P[6..-1]-P[1..-6]:
%p J:= select(t -> nops(convert(Q[t..t+4],set))=1, [$1..nops(Q)-4]):
%p P[J]; # _Robert Israel_, Oct 09 2017
%t Select[Partition[Prime@ Range[10^6], 10, 1], Equal[#10 - #5, #9 - #4, #8 - #3, #7 - #2, #6 - #1] & @@ # &][[All, 1]] (* _Michael De Vlieger_, Oct 08 2017 *)
%t udQ[n_]:=Length[Union[Differences[TakeDrop[n,5]][[1]]]]==1; Select[ Partition[ Prime[ Range[360000]],10,1],udQ][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 19 2018 *)
%o (PARI) for(n = 1, 50000, a = prime(n); b = prime(n+1); c = prime(n+2); d = prime(n+3); e = prime(n+4); f = prime(n+5); g = prime(n+6); h = prime(n+7); i = prime(n+8); j = prime(n+9); if((j - e)==(i - d) && (j - e)==(h - c) && (j - e)==(g - b) && (j - e)==(f - a), print1 (a," ,")));
%Y Cf. A000040, A292618, A292715, A292743.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Oct 08 2017