A093805 Numbers n with property that sum of digits is prime and number of prime digits is prime.

23, 25, 32, 52, 122, 133, 137, 155, 157, 173, 175, 203, 205, 212, 221, 223, 227, 229, 230, 232, 236, 238, 245, 247, 250, 254, 256, 263, 265, 272, 274, 278, 283, 287, 292, 302, 313, 317, 320, 322, 326, 328, 331, 335, 337, 353, 355, 359, 362, 371, 373, 377

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(1)=23, sum of digits 5 is prime, number of prime digits {2,3} 2 is prime,
a(5)=122, sum of digits 5 is prime, number of prime digits {2,2} 2 is prime,
a(10)=173, sum of digits 11 is prime, number of prime digits {3,7} is prime, ...

Maple

# Return list of digits stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i, ans) ]; od; RETURN(anstren); end: # Return number of prime digits ts_stpf:=proc(n) local i, stpf, ans, ans1; ans:=stev_sez(n): ans1:=[ ]: stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i, ans))='true') then stpf:=stpf+1; # stevilo prastevilskih stevk ans1:=[ op(ans1), op(i, ans) ]: # prastevilske stevke fi od; RETURN(stpf) end: # Return sum of digits ts_vsota_stevk:=proc(n) local i, stpf, ans, ans1; ans:=stev_sez(n): ans1:=[ ]: stpf:=0: for i from 1 to nops(ans) do stpf:=stpf+op(i, ans); od; RETURN(stpf) end: ts_pras_vsota_pra_stevk:=proc(n) local i, ans; ans:=[ ]: for i from 1 to n do if ( isprime(ts_vsota_stevk(i)) = 'true' and isprime(ts_stpf(i))='true') then ans:=[ op(ans), i ]: fi od; RETURN(ans) end: ts_pras_vsota_pra_stevk(2000);

Mathematica

sdpQ[n_]:=Module[{idn=IntegerDigits[n]}, And@@PrimeQ[{Total[idn], Count[ idn, _?PrimeQ]}]]; Select[Range[400], sdpQ] (* Harvey P. Dale, Oct 20 2013 *)

Crossrefs

Sequence in context: A054865 A054795 A305469 * A033629 A090311 A172015

Adjacent sequences: A093802 A093803 A093804 * A093806 A093807 A093808

Keyword

nonn,base

Author

Jani Melik, May 19 2004

Status

approved