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A260179 Primes pr(k) such that pr(k)+pr(k+1)+pr(k+6)+pr(k+7) = pr(k+2)+pr(k+3)+pr(k+4)+pr(k+5).

%I A260179 #19 May 06 2020 01:47:22
%S A260179 17,23,71,149,173,233,331,359,389,419,431,503,677,727,839,853,937,971,
%T A260179 1019,1201,1229,1277,1327,2213,2221,2237,2593,2689,2797,2999,3019,
%U A260179 3167,3221,3253,3821,3823,4027,4111,4201,4219,4231,4801,5147,5309,5407,5437
%N A260179 Primes pr(k) such that pr(k)+pr(k+1)+pr(k+6)+pr(k+7) = pr(k+2)+pr(k+3)+pr(k+4)+pr(k+5).
%H A260179 Amiram Eldar, <a href="/A260179/b260179.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..500 from R. J. Mathar)
%e A260179 Starting from 71, the eight consecutive primes are 71, 73, 79, 83, 89, 97, 101, 103; and they satisfy 71+73+101+103=79+83+89+97, so 71 is in the sequence.
%p A260179 n := 1 ;
%p A260179 Lp := [[0,1,6,7],[2,3,4,5]] ;
%p A260179 for i from 1 do
%p A260179     if add(ithprime(i+j),j=op(1,Lp)) = add(ithprime(i+j),j=op(2,Lp)) then
%p A260179         printf("%d %d\n",n,ithprime(i)) ;
%p A260179         n := n+1 ;
%p A260179     end if;
%p A260179 end do: # _R. J. Mathar_, Aug 06 2015
%t A260179 pr8Q[lst_]:=With[{tadr=TakeDrop[lst,{3,6}]},Total[tadr[[1]]] == Total[ tadr[[2]]]]; Transpose[Select[Partition[Prime[ Range[ 1000]],8,1], pr8Q]][[1]] (* The program uses the TakeDrop function from Mathematica version 10.2 *)
%Y A260179 Cf. A022885.
%K A260179 nonn
%O A260179 1,1
%A A260179 _Harvey P. Dale_, Jul 17 2015