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.
a(1)=2^0=1, a(2)=4^1=4, a(3)=6^3=216, a(4)=12^5=248832.
For n = 72, the smallest single or isolated number in the sequence 1, 73, 145, 217, 289, 361, 433, 505, 577, ... is 577, so a(72) = 577.
lista(pmax) = {my(p1 = 2, p2 = 3, c = 1); print1(c, ", "); forprime(p3 = 5, pmax, if(p2 == p1 + 2, c++; if(!((p1+1)%c), print1(c, ", "))); if(p2 != p1 + 2 && p2 != p3 - 2, c++); p1 = p2; p2 = p3);} \\ Amiram Eldar, May 17 2024
isA007510 := proc(n) if isprime(n) then not isprime(n-2) and not isprime(n+2) ; else false; end if ; end proc: isA014574 := proc(n) isprime(n+1) and isprime(n-1) ; end proc: isA167706 := proc(n) isA007510(n) or isA014574(n) ; end proc: isA005117 := proc(n) n =1 or numtheory[issqrfree](n) ; end proc: isA168270 := proc(n) isA005117(n) and isA167706(n) ; end proc: for n from 1 to 600 do if isA168270(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Dec 09 2009
a(1)=A167706(5)+A167706(6)=18+23=41.
a(1)=1+0=1, a(2)=2+4=6, a(3)=3+5=8.
A167706 := proc(n) if n = 1 then 2; else for a from procname(n-1)+1 do if isA007510(a) or isA014574(a) then return a; end if; end do; end if; end proc: for n from 1 to 110 do p := A167706(n) ; if isprime(p) then printf("%d,",n) : end if; end do: # R. J. Mathar, May 23 2010
a(1) = A167706(2) = (A167706(2-1) + A167706(2+1))/2 = (2 + 6)/2 = 4.
With[{nn = 560}, Function[s, Part[s, #] & /@ Select[Range[Length@ s - 1], Mean@{s[[# - 1]], s[[# + 1]]} == s[[#]] &]]@ Prepend[Union[Transpose[ Select[Partition[Prime@ Range@ nn, 3, 1], And[#[[2]] - #[[1]] != 2, #[[3]] - #[[2]] != 2] &]][[2]], Map[Mean, Select[Partition[Prime@ Range@ nn, 2, 1], Differences@ # == {2} &]]], 2]] (* Michael De Vlieger, Feb 22 2017, after Harvey P. Dale at A007510 and A014574 *)
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