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A073754
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Number of steps needed to reach a prime when the following map is repeatedly applied to n: if n is even then 2n + #(n) + 1, otherwise 2n - #(n) - 1, where #(n) is the number of digits of n; or -1 is no prime is ever reached.
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5
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3, 3, 2, 12, 2, 10, 11, 3, 1, 1, 9, 1, 1, 9, 2, 1, 10, 2, 1, 10, 1, 1, 8, 1, 2, 8, 1, 2, 13, 1, 1, 13, 1, 1, 9, 1, 1, 9, 1, 1, 35, 1, 2, 35, 8, 2, 7, 8, 1, 7, 1, 1, 52, 1, 6, 52, 21, 6, 12, 21, 1, 12, 1, 1, 12, 1, 1, 12, 28, 1, 8, 28, 1, 8, 5, 1, 6, 5, 1, 6, 1, 1, 34, 1, 5, 34, 1, 5, 71, 1, 7
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OFFSET
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2,1
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LINKS
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EXAMPLE
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For n=9, a(9)=3 because 9 -> 16 -> 35 -> 67
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MATHEMATICA
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pa[n_] := If[EvenQ[n], 2*n + IntegerLength[n] + 1, 2*n - IntegerLength[n] - 1]; Table[c = 0; If[PrimeQ[n], n = pa[n]; c = 1]; While[! PrimeQ[n] && c < 1000, n = pa[n]; c += 1]; If[c == 1000, c = -1]; c, {n, 2, 92}] (* Jayanta Basu, Jul 09 2013 *)
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PROG
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(UBASIC)
10 cls
30 for I=2 to 100
32 H=I
40 if odd(H)=1 then goto 90 else goto 50
50 A=2*H+alen(H)+1:K=K+1
60 if prmdiv(A)=A then print I, K:goto 120
65 if K>1000 then print I, 0:goto 120
70 H=A:goto 40
90 A=2*H-alen(H)-1:K=K+1
100 if prmdiv(A)=A then print I, K:goto 120
105 if K>1000 then print I, 0:goto 120
110 H=A:goto 40
120 K=0
130 next
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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