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 A164960 The minimum number of steps needed to generate prime(n) under the map x -> A060264(x) starting from any x taken from {2,3} or from A164333. 3
 0, 0, 1, 1, 2, 0, 2, 0, 3, 1, 0, 3, 1, 0, 4, 0, 2, 0, 1, 0, 0, 4, 2, 1, 5, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 5, 3, 0, 2, 0, 0, 0, 6, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 3, 1, 0, 0, 1, 0, 0, 1, 6, 4, 1, 0, 0, 3, 1, 0, 0, 1, 1, 7, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS V. Shevelev, On critical small intervals containing primes arXiv:0908.2319 EXAMPLE a(3) = 1  because prime(3)=5 can be generated in 1 step starting from x=2. a(4) = 1 because prime(4) =7 can be generated in 1 step starting from x=3. MAPLE # include source from A164333 and A060264 here A164333 := proc(n)         if n = 1 then                 13;         else                 for a from procname(n-1)+1 do                         if isA164333(a) then                                 return a;                         end if;                 end do;         end if; end proc: A164960aux := proc(p, strt)         local a, x;         if strt > p then                 return 1000000000;         end if;         a := 0 ;         x := strt ;         while x < p do                 x := A060264(x) ;                 a := a+1 ;         end do;         if x = p then                 return a ;         else                 return 1000000000;         end if; end proc: A164960 := proc(n)         local p, a, strt, i;         p := ithprime(n) ;         a := A164960aux(p, 2) ;         a := min(a, A164960aux(p, 3)) ;         for i from 1 do                 strt := A164333(i) ;                 if strt > p then                         return a;                 else                         a := min(a, A164960aux(p, strt)) ;                 end if;         end do:         return a; end proc: seq(A164960(n), n=1..90) ; # R. J. Mathar, Oct 29 2011 MATHEMATICA nmax = 100; kmax = nmax + 5; A164333 = Select[Table[{(Prime[k - 1] + 1)/2, (Prime[k] - 1)/2}, {k, 3, kmax}], AllTrue[Range[#[[1]], #[[2]]], CompositeQ] &][[All, 2]]*2 + 1; A164960aux[p_, strt_] := Module[{a, x}, If[strt > p, Return[10^9]]; a = 0; x = strt; While[x < p, x = NextPrime[2 x]; a++]; If[x == p, Return[a], Return[10^9]]]; A164960[n_] := Module[{p, a, strt, i}, p = Prime[n]; a = A164960aux[p, 2]; a = Min[a, A164960aux[p, 3]]; For[i = 1, i < 100, i++, strt = A164333[[i]]; If[strt > p, Return[a], a = Min[a, A164960aux[p, strt]]]]; Return[a]]; Table[A164960[n], {n, 1, nmax}] (* Jean-François Alcover, Dec 13 2017, after R. J. Mathar *) CROSSREFS Cf. A164333. Sequence in context: A094098 A261079 A182485 * A124137 A164092 A302643 Adjacent sequences:  A164957 A164958 A164959 * A164961 A164962 A164963 KEYWORD nonn AUTHOR Vladimir Shevelev, Sep 02 2009 EXTENSIONS One term corrected, sequence extended, examples added by R. J. Mathar, Oct 29 2011 STATUS approved

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Last modified November 19 04:39 EST 2018. Contains 317333 sequences. (Running on oeis4.)