A235725 - OEIS

%I #21 Jan 18 2014 09:50:28

%S 5,353,541,853,2341,4217,4229,8219,10663,11047,13591,18593,21577,

%T 28387,30181,34457,37853,52021,55333,57203,75389,84431,93229,110603,

%U 120811,147451,153499,162907,166357,176797,179581,219953,243671,246203,307253,342037,359701

%N Values k(i) such that k(i) + k(i+3) = k(i+1) + k(i+2), where k(i) is A022885(i).

%H Peter J. C. Moses, <a href="/A235725/b235725.txt">Table of n, a(n) for n = 1..5000</a>

%e Four consecutive Kimberling primes(A022885), beginning with 5 are 5,7,11,13. Since 5+13 = 7+11, then 5 is in the sequence; four consecutive Kimberling primes, beginning with 7 are 7,11,13,23. Since 7+23 is not equal to 11+13, then 7 is not in the sequence.

%t Nest[Map[#[[1]]&,Select[Partition[#,4,1],#[[1]]+#[[4]]==#[[2]]+#[[3]]&]]&,Prime[Range[5000]],2]

%o (PARI) isA022885(p) = {my(k = primepi(p)); (p == prime(k)) && ((prime(k) + prime(k+3)) == (prime(k+1) + prime(k+2)));}

%o lista(nn) = {prm = primes(nn); vkp = select(p->isA022885(p), prm); for(n=1, #vkp-3, if ((vkp[n] + vkp[n+3]) == (vkp[n+1] + vkp[n+2]), print1(vkp[n], ", ")););}  \\ _Michel Marcus_, Jan 15 2014

%Y Cf. A022885.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jan 15 2014

%E a(5)-a(37) from _Giovanni Resta_, Jan 15 2014