This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
(* see programming in A075275 *)
For the 1st term, 3! is in the middle between its closest prime neighbors 5 and 7. For the 2nd term, 5! is in the middle between its closest prime neighbors 113 and 127. From _Jon E. Schoenfield_, Jan 14 2022: (Start) In the table below, k = a(n), k! - d and k! + d are the two closest primes to k!, and d = A033932(k) = A033933(k) = A053711(n): . n k d - ---- ---- 1 3 1 2 5 7 3 10 11 4 21 31 5 171 397 6 190 409 7 348 1657 8 1638 2131 9 3329 7607 (End)
for n from 3 to 200 do j := n!-prevprime(n!): if not isprime(n!+j) then next fi: i := 1: while not isprime(n!+i) and (i<=j) do i := i+2 od: if i=j then print(n):fi:od:
PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k] Do[ a = n!; If[2a == PrevPrim[a] + NextPrim[a], Print[n]], {n, 3, 415}]
a(4) = 3 because 4!! = 8 and 8 -/+ 3 = 5 and 11 are primes with smallest equal distances from 4!!
smbp[n_]:=Module[{m=0,n2=n!!},While[Total[Boole[PrimeQ[n2+{m,-m}]]] != 2,m++];m]; Array[smbp,60,2] (* Harvey P. Dale, Sep 02 2017 *)
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