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A337489
a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)) sets a new record. A337488 are the corresponding values of k.
6
3, 7, 29, 113, 523, 1151, 1327, 9551, 15683, 19609, 25471, 31397, 156007, 360653, 370261, 492113, 1349533, 1357201, 1357333, 1562051, 2010733, 4652507, 17051707, 17051887, 20831323, 47326693, 47326913, 122164747, 189695893, 191912783, 387096133, 428045741, 436273291
OFFSET
1,1
EXAMPLE
List of first terms:
a(n) pi(a(n)) average-median
3, 2, 1/3 = (2 + 3 + 5)/3 - 3
7, 4, 2/3 = (5 + 7 + 11)/3 - 7
29, 10, -4/3 = (23 + 29 + 31)/3 - 29
113, 30, 10/3
523, 99, 16/3
1151, 190, -20/3
1327, 217, 28/3
9551, 1183, 32/3
PROG
(PARI) a337489(limp) = {my(p1=0, p2=2, p3=3, s=p1+p2+p3, d=0); forprime(p=5, limp, s=s-p1+p; my(dd=abs(s/3-p3)); if(dd>d, print1(p3, ", "); d=dd); p1=p2; p2=p3; p3=p)};
a337489(500000000)
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Aug 29 2020
STATUS
approved