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 A182782 a(n) is one less than the length of the sequence b(n) defined by: b(1) = n; for k > 1, b(k+1) is the smallest prime factor of 1+b(k)^2 not already in the b-sequence. 1
 11, 10, 11, 4, 1, 9, 11, 2, 11, 12, 11, 2, 2, 12, 11, 12, 3, 2, 11, 7, 11, 2, 11, 12, 11, 12, 11, 2, 4, 4, 11, 2, 11, 3, 11, 12, 8, 2, 11, 12, 43, 2, 11, 3, 11, 5, 11, 2, 11, 44, 11, 2, 11, 12, 11, 12, 11, 2, 11, 3, 11, 2, 11, 4, 11, 12, 11, 2, 11, 3, 11, 2, 11, 12, 11, 12, 11, 2, 11, 9, 11, 2, 11, 12, 11, 3, 11, 2, 11, 12, 11, 2, 11, 12, 11, 3, 11, 2, 11, 12, 11, 2, 11, 5, 11, 4, 11, 2, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The number of terms of each sequence b(n) is finite. Records are a(1)=11, a(10)=12, a(41)=43, a(50)=44, and apparently no others; i.e., the next is not smaller than n=360000 if it exists. LINKS EXAMPLE a(1) = 11 counts the iterations in the b-chain 1 -> 2 -> 5 -> 13 -> 17 -> 29 -> 421 -> 401 -> 37 -> 137 -> 1877 -> 41 (end of the cycle because 41 -> 29). In detail the chain is computed as follows: 1^2 + 1 = 2; 2^2 + 1 = 5; 5^2 + 1 = 2*13 -> 13 because 2 is already in the sequence; 13^2 + 1 = 2*5*17 -> 17 because 2 and 5 are already in the sequence; 17^2 + 1 = 2*5*29 -> 29; 29^2 + 1 = 2*421 -> 421; 421^2 + 1 = 2*13*17*401 -> 401; 401^2 + 1 = 2*37*41*53 -> 37; 37^2 + 1 = 2*5*137 -> 137; 137^2 + 1 = 2*5*1877 -> 1877; 1877^2 + 1 = 2*5*13*41*661 -> 41 (end of the cycle because 41^2 + 1 = 2*29^2 -> 29 is already in the sequence). MAPLE A182782b := proc(n)         local bcyc, pfs , b2;         bcyc := [n] ;         while true do                 b2 := op(-1, bcyc) ;                 pfs := sort(convert(numtheory[factorset](1+b2^2), list)) ;                 endcy := true;                 for f in pfs do                         if not member(f, bcyc)  then                                 endcy := false;                                 bcyc := [op(bcyc), f] ;                                 break;                         end if;                 end do:                 if endcy then                         return bcyc ;                 end if;         end do; end proc: A182782 := proc(n)         nops(A182782b(n))-1 ; end proc: # R. J. Mathar, Feb 06 2011 CROSSREFS Sequence in context: A070561 A059941 A086100 * A217789 A004283 A106421 Adjacent sequences:  A182779 A182780 A182781 * A182783 A182784 A182785 KEYWORD nonn AUTHOR Michel Lagneau, Feb 01 2011 STATUS approved

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Last modified October 16 13:32 EDT 2019. Contains 328093 sequences. (Running on oeis4.)