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.
3$ + 1 = 7 is prime, so 7 is in the sequence. (Here '$' denotes the swinging factorial function.)
# Seq with arguments <= n: a := proc(n) select(isprime,map(x -> A056040(x)+1,[$1..n])); select(isprime,map(x -> A056040(x)-1,[$1..n])); sort(convert(convert(%%,set) union convert(%,set),list)) end:
Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f - 1], Sow[p]]; If[PrimeQ[p = f + 1], Sow[p]], {n, 1, 45}]][[2, 1]] // Union (* Jean-François Alcover, Jun 28 2013 *)
17 is a term because 17 - 1 = 16 is a number of least prime signature.
{2}~Join~Select[Prime@ Range[2, 900], AnyTrue[# + {-1, 1}, Times @@ MapIndexed[Prime[First[#2]]^#1 &, Sort[FactorInteger[#][[All, -1]], Greater] ] == # &] &] (* Michael De Vlieger, May 16 2021 *)
a(1)=2 because (2-2)! + 1 = 0! + 1 = 1 + 1 = 2.
aa = {}; Do[p = Prime[n]; If[PrimeQ[(p - 2)! + 1], AppendTo[aa, p]], {n, 1, 10000}]; aa
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