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A215647 Smallest semiprime whose decimal expansion consists of the concatenation of a 1-digit semiprime, a 2-digit semiprime, a 3-digit semiprime, ..., and an n-digit semiprime. 10
4, 415, 410111, 4101061003, 410106100310003, 410106100310001100001, 4101061003100011000011000057, 410106100310001100001100000110000051, 410106100310001100001100000110000001100000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is to A215641 as semiprimes A001358 are to primes A000040. It is a plausible conjecture that a(n) always exists.

If a(n) exists it has A000217(n) = n(n+1)/2 digits.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

a(2) = 415 = 5 * 83 = concatenation of 4 and 15, where 4 is the semiprime 2^2 and 15 is the semiprime 3 * 5.

a(3) = 410111 = 13 * 31547 = the concatenation of 4, 10, and 111 where 4 = 2^2, 10 = 2 * 5, and 111 = 3 * 37.

a(5) = 410106100310003 = 76871 * 5334991093 = Concatenate(4,10,106,1003,10003).

CROSSREFS

Cf. A001358, A215641.

Sequence in context: A198709 A326209 A287965 * A228242 A036771 A201980

Adjacent sequences: A215644 A215645 A215646 * A215648 A215649 A215650

KEYWORD

nonn,base

AUTHOR

Jonathan Vos Post, Aug 19 2012

STATUS

approved

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Last modified November 26 13:43 EST 2022. Contains 358362 sequences. (Running on oeis4.)