A173620 - OEIS

A173620

Main diagonal of array A[k,n] = n-th Fibonacci number which becomes prime when digits (base k) are reversed.

%I #7 Jan 16 2018 02:46:55

%S 2,5,13,8,89,233,233,1597,39088169,121393,4052739537881

%N Main diagonal of array A[k,n] = n-th Fibonacci number which becomes prime when digits (base k) are reversed.

%C First row is the prime Fibonacci numbers A005478 (as reverse of unary does not change the number). 10th row is A173268. Computations mostly by _R. J. Mathar_ after first few terms from _Jonathan Vos Post_. Mathar also notes that omitting the base=1 row, gives the diagonal: 3, 5, 5, 55, 34, 89, 610, 1346269, 75025, 2504730781961, 14930352. The array begins:

%C ===============================================================================

%C ....|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.....n=7.|...n=8.|........n=9.|......n=10|

%C k=1.|..2...|..3.|...5.|..13.|..89.|.233.|....1597.|...28657.|...514229.|.433494437|

%C k=2.|..3...|..5.|..13.|..34.|..55.|.233.|.....377.|.....610.|.....2584.|...4181657|

%C k=3.|..2...|..5.|..13.|..21.|..55.|.233.|.....987.|...28657.|....75025.|.433494437|

%C k=4.|..2...|..3.|...5.|...8.|..13.|..89.|.....233.|....1597.|.....4181.|....514229|

%C k=5.|..2...|..3.|..13.|..55.|..89.|.233.|...28657.|...21393.|...514229.|...9227465|

%C k=6.|..2...|..3.|...5.|...8.|..34.|.233.|14930352.|63245986.|701408733|...86267571272.

%C k=7.|..2...|..3.|...5.|..13.|..21.|..89.|.....233.|....1597.|.....4181|....2865

%C k=8.|..2...|..3.|...5.|..13.|..89.|.233.|.....610.|....1597.|.....2584|.....4181

%C k=9.|..2...|..3.|...5.|..13.|..21.|.987.|....1597.|..346269.|.39088169|701408733

%C k=10|..2...|..3.|...5.|..13.|..34.|.377.|....1597.|...10946.|....75025|121393|

%C k=11|.2..3....5.....13.....55......89.......233.........1597..956722026041.2504730781961.4052739537881

%C k=12|.2..3....5.....13.....21......89......1597......1346269......3524578.......5702887.....14930352.4052739537881.

%C k=13|.2..3....5.....55.....89.....233.......377.........1597........75025.

%C k=14|.2..3....5.....13...2584....4181..39088169.365435296162.956722026041.

%C k=15|.2..3....5.....13....233.....377......1597.........4181.........6765.........75025.......121393....701408733.956722026041

%Y Cf. A000040, A000045, A001605, A004086, A115347, A173268.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Feb 22 2010