A106551 - OEIS

%I #18 Jun 10 2020 05:38:58

%S 26,38,42,62,86,68,94,134,80,158,146,206,110,230,172,278,126,224,170,

%T 250,350,374,200,302,446,194,494,260,518,380,228,406,566,290,638,484,

%U 350,710,296,1232,734,536,562,330,806,614,854,1454,440,878,470,950,692

%N a(n) = n-th semiprime + (concatenation of its two divisors, largest divisor first).

%C Concatenation of the divisors starting with the smallest one leads to a different sequence.

%H Robert Israel, <a href="/A106551/b106551.txt">Table of n, a(n) for n = 1..10000</a>

%e First semiprime is 4; 4 is 2*2; 26=4+22.

%e Second semiprime is 6; 6 is 3*2; 38=6+32.

%e Third semiprime is 9; 9 is 3*3; 42=9+33.

%e Fourth semiprime is 10; 10 is 5*2; 62=10+52.

%p N:= 1000: # for terms <= N

%p Primes:= select(isprime,[2,seq(i,i=3..N/2,2)]):

%p R:= NULL:

%p for i from 1 to nops(Primes) do for j from 1 to i while Primes[i]*Primes[j] <= N do

%p   R:= R, [Primes[i]*Primes[j],Primes[i]*10^(1+ilog10(Primes[j]))+Primes[j]]

%p od od:

%p map(convert,sort([R],(x,y) -> x[1]<y[1]),`+`); # _Robert Israel_, Jun 09 2020

%t cp[n_] := Block[{p = Reverse[ First /@ FactorInteger[ n]]}, If[ Length[p] == 1, p = Join[p, p]]; n + FromDigits[ Join @@ IntegerDigits@p]]; cp /@ Select[ Range@ 160, 2 == PrimeOmega@ # &] (* _Giovanni Resta_, Jun 10 2020 *)

%K base,easy,nonn,look

%O 1,1

%A _Eric Angelini_, May 09 2005

%E Edited by _N. J. A. Sloane_, Sep 29 2007

%E Corrected and extended by _Harvey P. Dale_, Jun 03 2012

%E a(40) and a(48) corrected by _Robert Israel_, Jun 09 2020