A103607 - OEIS

%I #15 Sep 01 2024 03:56:36

%S 4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,49,51,55,57,58,62,65,74,77,

%T 82,85,86,87,91,93,94,95,106,111,115,118,119,121,122,123,129,133,134,

%U 141,142,143,145,146,155,158,159,161,166,169,177,178,183,185,187

%N Write down the semiprimes but omit any semiprime (such as 46 or 69) that is the concatenation of consecutive semiprimes.

%C The complement of this sequence is the sequence of semiprimes which are concatenations of successive semiprimes.

%C Note that this sequence is not analogous to A119615 for two reasons. In A119615 partial concatenation is taken into account, i.e., the terms 7, 11 prevent 71 to be included, while here only full concatenation is considered (hence 58, 62 do not forbid 86). Moreover in A119615 the terms to be concatenated are those in the sequence itself, while here are all the semiprimes. - _Giovanni Resta_, Jun 16 2016

%e 46 is not a term because concatenate(sp(1),sp(2)) = 46 = 2 * 23.

%e 69 is not a term because concatenate(sp(2),sp(3)) = 69 = 3 * 23.

%e 469 is not a term because concatenate(sp(1),sp(2),sp(3)) = 469 = 7 * 67.

%e 1415 is not a term because concatenate(sp(5),sp(6)) = 1415 = 5 * 283.

%e 2122 is not a term because concatenate(sp(7),sp(8)) = 2122 = 2 * 1061.

%e 3839 is not a term because concatenate(sp(14),sp(15)) = 3839 = 11 * 349.

%e 469101415 is not a term because concatenate(sp(1),sp(2),sp(3),sp(4),sp(5),sp(6)) = 469101415 = 5 * 93820283.

%e Where sp(i) is A001358(i).

%Y Cf. A001358, A048991, A119615.

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jun 07 2006

%E Name edited by _Giovanni Resta_, Jun 16 2016