A082770 -id:A082770 - cp's OEIS frontend

A082768 Numbers that begin with 1, 3, 7 or 9.

1, 3, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset: 1

Amarnath Murthy, Apr 18 2003

Cf. A082769, A082770, A045572 (Numbers that end with 1, 3, 7 or 9).

Cf. A082769, A082770, A089743.

isA082768 := proc(n)
    convert(n,base,10) ;
    if op(-1,%) in {1,3,7,9} then
        true;
    else
        false;
    end if;
end proc:
A082768 := proc(n)
    if n = 1 then
        1;
    else
        for a from procname(n-1)+ 1 do
            if isA082768(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A082768(n),n=1..120) ; # R. J. Mathar, Aug 27 2025

Select[Range[119], MemberQ[{1, 3, 7, 9}, First[IntegerDigits[#]]] &] (* Jayanta Basu, Jun 24 2013 *)

More terms from David Wasserman, Jul 28 2005

Offset changed by Andrew Howroyd, Sep 29 2024

A082769 a(n) = smallest palindromic prime that begins with A082768(n), or 0 if no such number exists.

Original entry on oeis.org

11, 3, 7, 919, 101, 11, 12421, 131, 14341, 151, 16061, 17471, 181, 191, 30103, 313, 32323, 33533, 34543, 353, 36263, 373, 383, 39293, 70207, 71317, 727, 73037, 74047, 757, 76367, 77377, 787, 797, 90709, 919, 929, 93139, 94049, 95959, 96269, 97379, 98389, 9902099, 1003001, 101, 1022201, 10301, 1043401, 10501, 10601, 1074701, 1082801, 1092901

Offset: 1

Amarnath Murthy, Apr 18 2003

Conjecture: no entry is zero.

Cf. A082768, A082770.

ispali := proc(n,b)
    local dgs,i ;
    dgs := convert(n,base,b) ;
    for i from 1 to nops(dgs)/2 do
        if op(i,dgs) <> op(-i,dgs) then
            return false;
        end if;
    end do:
    true;
end proc:
L082768 := [seq(A082768(n),n=1..200)] ; # use code in A082768
L082769 := [seq(0,n=1..200)] ;
for pi from 2 do
    p :=ithprime(pi) ;
    if ispali(p,10) then
        pdgs := convert(p,base,10) ;
        for sh from 0 do
            restp := add(op(i,pdgs)*10^(i-1),i=1..nops(pdgs)) ;
            for i from 1 to nops(L082768) do
                if op(i,L082768) = restp then
                    if op(i,L082769) = 0 then
                        L082769 := subsop(i=p,L082769) ;
                        print(L082769) ;
                    end if;
                end if;
            end do:
            # chop digits from palindromic prime starting at least signif
            pdgs := subsop(1=NULL,pdgs) ;
            if nops(pdgs) = 0 then
                break ;
            end if;
        end do:
    end if;
end do: # R. J. Mathar, Aug 27 2025

More terms from David Wasserman, Jul 28 2005

12 more terms from R. J. Mathar, Aug 27 2025

cp's OEIS Frontend

A082768 Numbers that begin with 1, 3, 7 or 9.

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

Extensions