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A055381
Smallest composite k such that the n closest primes below and above k are symmetric about k.
13
4, 9, 12, 30, 30, 165, 8021811, 1071065190, 1613902650, 1797595815015, 633925574060895, 22930603692243585
OFFSET
1,1
COMMENTS
Center of the smallest 2n-tuple of consecutive odd primes with symmetrical gaps (cf. A055382).
LINKS
Carlos Rivera, Problem 60. Symmetric primes on each side, The Prime Puzzles & Problems Connection.
FORMULA
a(n) = ( A055382(n) + A000040(A000720(A055382(n))+2n) ) / 2 = ( A055382(n) + A151800(...(A151800(A055382(n)))...) ) / 2, where A151800 is iterated 2n times. - Max Alekseyev, Jul 23 2015
a(n) = (A000040(m) + A000040(m+1))/2, where m = min( {k >= 2 : A359440(k) >= n-1} ). - Peter Munn, Jan 09 2023
EXAMPLE
The three primes on each side of 12 (13, 17, 19 and 11, 7, 5) are symmetrical with respect to the gaps, so a(3) = 12.
MATHEMATICA
Table[i = n + 2;
While[x =
Differences@
Flatten@{Table[NextPrime[i, k], {k, -n, -1}], i,
Table[NextPrime[i, k], {k, 1, n}]}; x != Reverse[x],
i++]; i, {n, 6}] (* Robert Price, Oct 12 2019 *)
KEYWORD
nonn,more,hard
AUTHOR
Jud McCranie, Jun 23 2000
EXTENSIONS
a(10) from Donovan Johnson, Mar 09 2008
a(11) from Dmitry Petukhov, added by Max Alekseyev, Aug 08 2014
a(12) computed from A055382(12) by Max Alekseyev, Jul 23 2015
Name clarified by Peter Munn, Jan 09 2023
STATUS
approved