A278455 Smallest prime that takes n steps to get to 1, each step reducing the prime by the largest power of 2 possible, with the resultant number a prime.

3, 7, 23, 61, 317, 829, 274973, 1844867, 29363357, 275684009603, 2252075497694851, 1155173580104541827, 155838096186773789746819, 649037426474450432457432557949469, 348449144376078413060946030467563206480413

Offset: 1

Author

Randy L. Ekl, Nov 22 2016

Keywords

• nonn
• base

Examples

			61 is the smallest prime with 4 steps: 61 (-32) -> 29 (-16) -> 13 (-8) -> 5 (-4) -> 1.
23 is the smallest prime with 3 steps: 23 -> 7 -> 3 -> 1
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..18

Crossrefs

Cf. A278454.

Programs

Magma

a:=[]; A:=[<1,0>]; /* A[j] is a pair: (A278454(j-1) & its no. of steps) */ maxSteps:=0; for d in [1..60] do for j in [1..#A] do t:=2^d+A[j][1]; if IsPrime(t) then A[#A+1]:=; if A[#A][2] gt maxSteps then maxSteps:=A[#A][2]; a[#a+1]:=A[#A][1]; end if; end if; end for; end for; a; //Jon E. Schoenfield, Nov 23 2016

Mathematica

First /@ DeleteDuplicatesBy[#, Last] &@ Map[{First@ #, Length@ # - 1} &, DeleteCases[Map[NestWhileList[# - 2^Floor@ Log2@ # &, #, # > 1 &] &, Prime@ Range[2, 200000]], w_ /; Times @@ Boole[PrimeQ /@ Most@ w] != 1]] (* Michael De Vlieger, Nov 22 2016 *)

Extensions

a(10)-a(15) from Jon E. Schoenfield, Nov 22 2016