A118688 Semiprimes for which the sum of the digits is also a semiprime.

4, 6, 9, 15, 22, 33, 46, 51, 55, 69, 77, 82, 86, 87, 91, 95, 118, 121, 123, 141, 145, 158, 159, 177, 185, 194, 202, 213, 217, 226, 235, 249, 253, 262, 267, 301, 303, 321, 329, 334, 339, 361, 365, 393, 411, 415, 437, 446, 447, 451, 473, 482, 489, 501, 505, 514

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), May 20 2006

Keywords

• base
• nonn

Comments

The first term congruent to 2 mod 9 is a(2729) = 29999. - Robert Israel, Jul 07 2015

Among first 10000 terms, numbers of terms congruent to {0..8} mod 9 are: {1,425,139,1453,2773,1233,1252,3087,2739}. Terms with minimal digitsum = 4 are: {4,22,121,202,301,1003,1111,2101,10003, 10021,10102,10201,11002,11101,12001,30001,100021,100102,100201,101011, 110002,110101,111001}. Is this subsequence infinite? - Zak Seidov, Jul 07 2015

Examples

			55 is in the sequence because (1) it is a semiprime and (2) the sum of its digits 5+5=10 is also a semiprime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A007953.

Programs

Maple

select(t -> map(numtheory:-bigomega,[t,convert(convert(t,base,10),`+`)])=[2,2], [$1..1000]); # Robert Israel, Jul 07 2015

Mathematica

Select[Range[514],PrimeOmega[{Total[IntegerDigits[#]],#}]=={2,2}&] (* Zak Seidov, Jul 07 2015 *)

PARI

A007953(n)= { local(resul); resul=0; while(n>0, resul += n%10; n = (n-n%10)/10; ); return(resul); } { for(n=4,600, if( bigomega(n)==2, if(bigomega(A007953(n)) == 2, print1(n,","); ); ); ); } \\ R. J. Mathar, May 23 2006

Extensions

Corrected by R. J. Mathar, May 23 2006