A230820 Table, read by antidiagonals, of palindromic primes in base b expressed in decimal.

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

Links

Table of n, a(n) for n=1..66.

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

Crossrefs

Cf. A000040, A016041, A029971, A029972, A029973, A029974, A029975, A029976, A029977, A002385, A029978, A029979, A029980, A029981, A029982, A029732, A182231.

Sequence in context: A046227 A120842 A319044 * A324549 A152178 A274164

Adjacent sequences: A230817 A230818 A230819 * A230821 A230822 A230823

Keyword

nonn,base,easy,tabl

Author

Robert G. Wilson v, Oct 30 2013

Status

approved