A235725 Values k(i) such that k(i) + k(i+3) = k(i+1) + k(i+2), where k(i) is A022885(i).

5, 353, 541, 853, 2341, 4217, 4229, 8219, 10663, 11047, 13591, 18593, 21577, 28387, 30181, 34457, 37853, 52021, 55333, 57203, 75389, 84431, 93229, 110603, 120811, 147451, 153499, 162907, 166357, 176797, 179581, 219953, 243671, 246203, 307253, 342037, 359701

Offset: 1

Author

Vladimir Shevelev, Jan 15 2014

Keywords

• nonn

Examples

			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.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A022885.

Programs

Mathematica

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

PARI

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

Extensions

a(5)-a(37) from Giovanni Resta, Jan 15 2014