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A131317 Repdigit semiprimes. 2
22, 33, 55, 77, 111, 1111, 11111, 1111111, 11111111111, 11111111111111111, 2222222222222222222, 3333333333333333333, 5555555555555555555, 7777777777777777777, 22222222222222222222222, 33333333333333333333333 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A semiprime can be repdigit (base 10) in only two ways. It can be a repunit semiprime (A102782) or it can be a repunit prime times a prime digit {2, 3, 5, 7}. Subset of A046328. Subset of A116063. Occurs in proof that the sequence is infinite in which a(n) is the least semiprime > a(n-1) such that a(n) has no digit in common with a(n-1).

LINKS

Table of n, a(n) for n=1..16.

FORMULA

A102782 UNION 2*A004022 UNION 3*A004022 UNION 5*A004022 UNION 7*A004022.

EXAMPLE

a(1) = 22 = 2 * 11;

a(2) = 33 = 3 * 11;

a(3) = 55 = 5 * 11;

a(4) = 77 = 7 * 11;

a(5) = 111 = 3 * 37;

a(6) = 1111 = 11 * 101;

a(7) = 11111 = 41 * 271.

MATHEMATICA

Select[Flatten[Table[FromDigits[PadRight[{}, n, i]], {n, 2, 25}, {i, 9}]], PrimeOmega[#]==2&] (* Harvey P. Dale, Mar 07 2014 *)

CROSSREFS

Cf. A000042, A001358, A004023, A046413, A046328, A102782, A116063.

Sequence in context: A138840 A257473 A116063 * A176597 A067087 A155709

Adjacent sequences:  A131314 A131315 A131316 * A131318 A131319 A131320

KEYWORD

base,easy,nonn

AUTHOR

Jonathan Vos Post, Oct 21 2007

STATUS

approved

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Last modified July 2 16:02 EDT 2020. Contains 335404 sequences. (Running on oeis4.)