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

Author

Jonathan Vos Post, Feb 22 2010

Keywords

• nonn
• base

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:

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....|.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

Crossrefs

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