A098837 Smith semiprimes.

4, 22, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 382, 391, 454, 517, 526, 535, 562, 634, 706, 778, 895, 913, 922, 958, 985, 1111, 1165, 1219, 1255, 1282, 1507, 1633, 1642, 1678, 1795, 1822, 1858, 1894, 1903, 1921, 1966, 2038, 2155, 2173, 2182, 2218

Offset: 1

Author

Shyam Sunder Gupta, Oct 10 2004

Keywords

• base
• nonn

Examples

			a(3)=58 because 58 is a Smith number as well as a semiprime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157.

Crossrefs

Cf. A001358, A006753.

Programs

Maple

N:= 10000: # for terms <= N
P:= select(isprime, [2,seq(i,i=3..N/2,2)]):
nP:= nops(P):
sP:= map(p -> convert(convert(p,base,10),`+`), P):
Res:= {}:
for i from 1 to nP do
  for j from i to nP do
    n:= P[i]*P[j];
    if n > N then break fi;
    if convert(convert(n,base,10),`+`) = sP[i]+sP[j] then
      Res:= Res union {n}
    fi
od od:
sort(convert(Res,list)); # Robert Israel, Aug 24 2024

Mathematica

sspQ[n_]:=PrimeOmega[n]==2&&Total[Flatten[IntegerDigits/@(Table[#[[1]],#[[2]]]&/@FactorInteger[n])]]==Total[IntegerDigits[n]]; Select[Range[ 2220], sspQ] (* Harvey P. Dale, Jul 25 2019 *)

PARI

dsum(n)=my(s);while(n,s+=n%10;n\=10);s
list(lim)=my(v=List(),d); forprime(p=2, sqrt(lim), d=dsum(p); forprime(q=p, lim\p, if(d+dsum(q)==dsum(p*q),listput(v, p*q)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jan 03 2012