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A230820
Table, read by antidiagonals, of palindromic primes in base b expressed in decimal.
2
3, 2, 5, 2, 13, 7, 2, 3, 23, 17, 2, 3, 5, 151, 31, 2, 3, 31, 17, 173, 73, 2, 3, 5, 41, 29, 233, 107, 2, 3, 5, 7, 67, 59, 757, 127, 2, 3, 5, 71, 37, 83, 257, 937, 257, 2, 3, 5, 7, 107, 43, 109, 373, 1093, 313, 2, 3, 5, 7, 73, 157, 61, 701, 409, 1249, 443
OFFSET
1,1
EXAMPLE
\r
b\
.2.3...5...7...17...31...73..107..127...257...313...443..1193..1453..1571.=A016041
.3.2..13..23..151..173..233..757..937..1093..1249..1429..1487..1667..1733.=A029971
.4.2...3...5...17...29...59..257..373...409...461...509...787...839...887.=A029972
.5.2...3..31...41...67...83..109..701...911..1091..1171..1277..1327..1667.=A029973
.6.2...3...5....7...37...43...61...67...191...197..1297..1627..1663..1699.=A029974
.7.2...3...5...71..107..157..257..271...307..2549..2647..2801..3347..3697.=A029975
.8.2...3...5....7...73...89...97..113...211...227...251...349...373...463.=A029976
.9.2...3...5....7..109..127..173..191...227...337...373...419...601...619.=A029977
10.2...3...5....7...11..101..131..151...181...191...313...353...373...383.=A002385
11.2...3...5....7..199..277..421..443...499...521...587...643...709...743.=A029978
12.2...3...5....7...11...13..157..181...193...229...241...277...761...773.=A029979
...
inf..2..3..5..7..11..13..17..19..23..29..31..37..41..43..47..53..59..61...=A000040
MAPLE
A230820 := proc(b, n)
option remember;
local a, dgs ;
if n = 1 then
if b = 2 then
return 3;
else
return 2;
end if;
else
for a from procname(b, n-1)+1 do
if isprime(a) then
ispal := true ;
dgs := convert(a, base, b) ;
for i from 1 to nops(dgs)/2 do
if op(i, dgs) <> op(-i, dgs) then
ispal := false;
end if;
end do:
if ispal then
return a;
end if;
end if;
end do:
end if;
end proc:
for b from 2 to 9 do
for n from 1 to 9 do
printf("%3d ", A230820(b, n)) ;
end do:
printf("\n") ;
end do; # R. J. Mathar, Feb 16 2014
MATHEMATICA
palQ[n_Integer, base_Integer] := Module[{idn = IntegerDigits[ n, base]}, idn == Reverse@ idn]; Table[Select[Prime@Range@500, palQ[#, k + 1] &][[b - k + 1]], {b, 11}, {k, b, 1, -1}] // Flatten
KEYWORD
nonn,base,easy,tabl
AUTHOR
Robert G. Wilson v, Oct 30 2013
STATUS
approved