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A278455
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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.
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2
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3, 7, 23, 61, 317, 829, 274973, 1844867, 29363357, 275684009603, 2252075497694851, 1155173580104541827, 155838096186773789746819, 649037426474450432457432557949469, 348449144376078413060946030467563206480413
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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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LINKS
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Jon E. Schoenfield, Table of n, a(n) for n = 1..18
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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]:=<t, A[j][2]+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
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CROSSREFS
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Cf. A278454.
Sequence in context: A127178 A001275 A058757 * A060089 A148689 A148690
Adjacent sequences: A278452 A278453 A278454 * A278456 A278457 A278458
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KEYWORD
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nonn,base
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AUTHOR
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Randy L. Ekl, Nov 22 2016
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EXTENSIONS
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a(10)-a(15) from Jon E. Schoenfield, Nov 22 2016
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STATUS
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approved
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