A173620 Main diagonal of array A[k,n] = n-th Fibonacci number which becomes prime when digits (base k) are reversed.

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

Offset

1,1

Comments

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:

===============================================================================

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Links

Table of n, a(n) for n=1..11.

Crossrefs

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

Sequence in context: A243366 A139023 A241758 * A319920 A166134 A336883

Adjacent sequences: A173617 A173618 A173619 * A173621 A173622 A173623

Keyword

nonn,base

Author

Jonathan Vos Post, Feb 22 2010

Status

approved