A073754 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.

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

Offset

2,1

Links

Sean A. Irvine, Table of n, a(n) for n = 2..1000

Example

For n=9, a(9)=3 because 9 -> 16 -> 35 -> 67

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A330307 A256916 A164705 * A193229 A112458 A019252

Adjacent sequences: A073751 A073752 A073753 * A073755 A073756 A073757

Keyword

easy,nonn,base

Author

Felice Russo, Sep 02 2002

Extensions

More terms from Jason Earls, Sep 04 2002

Status

approved