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A105984 Near-repdigit semiprimes with 3 as repeated digit. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 14:29 EST 2020. Contains 338802 sequences. (Running on oeis4.)