A105984 Near-repdigit semiprimes with 3 as repeated digit.

133, 303, 323, 334, 335, 339, 393, 533, 633, 933, 1333, 3133, 3233, 3334, 3337, 3338, 3353, 3383, 4333, 6333, 8333, 13333, 30333, 33133, 33233, 33313, 33323, 33339, 33373, 33393, 33433, 33833, 33933, 35333, 37333, 43333, 73333, 83333, 133333

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1962

Example

a(2)=303 is a term because 303 is a semiprime and all digits are equal to 3 except one.

Mathematica

okQ[n_]:=DigitCount[n, 10, 3]==IntegerLength[n]-1&&n>99; upto=150000; p=Prime[Range[PrimePi[upto/2]]]; lim= Floor[Sqrt[upto]]; sp={}; k=0; While[k++; p[[k]]<=lim, sp=Join[sp, p[[k]]*Take[p, {k, PrimePi[upto/p[[k]]]}]]]; sp=Sort[sp]; Select[sp, okQ] (* Harvey P. Dale, Mar 18 2011; semiprime generating portion from A001358, Mar 15 2011 *)
s={}; Do[t3=Table[3, {k}]; Do[If[d ≠ 3, rep=FromDigits/@Permutations[Flatten@{t3, d}]; s=Join[s, Select[rep, 2==Plus@@Last/@FactorInteger[#]&]]], {d, 0, 9}], {k, 2, 13}]; Rest@Union@s (* Zak Seidov, Mar 18 2011 *)

Prog

(PARI) issemi(n)={ \\ Much faster tests are possible, this is a basic one
    forprime(p=2, min(1e5, n^(1/3)),
        if (n%p == 0, return (isprime(n\p)))
    );
    if (isprime(n), return(0));
    if (n < 1e15, return(1));
    my(f = factorint(n, 9));
    if (#f[, 1] > 2, return(0));
    if (#f[, 1] == 2,
        if (f[1, 2] + f[2, 2] > 2, return(0));
        return (isprime(f[1, 1]) && isprime(f[2, 1]))
    );
    bigomega(n) == 2
};
v=List(); for(l=3, 30, N=10^l\3; forstep(i=l-1, 0, -1, t=10^i; forstep(a=-3*t, 6*t, [t, t, 2*t, t, t, t, t, t], if(issemi(N+a)&N+a>33, listput(v, N+a))))); v=Vec(v)
\\ Charles R Greathouse IV, Mar 18 2011

Crossrefs

Sequence in context: A050882 A146233 A146181 * A115518 A064903 A259638

Adjacent sequences: A105981 A105982 A105983 * A105985 A105986 A105987

Keyword

base,nonn

Author

Shyam Sunder Gupta, Apr 29 2005

Status

approved