A093807 Palindromic numbers with property that sum of digits is prime and number of prime digits is prime.

212, 232, 272, 292, 313, 353, 373, 515, 535, 575, 595, 737, 757, 797, 12121, 12521, 12721, 13331, 13531, 13931, 15151, 15551, 15751, 17171, 17371, 17771, 20102, 20302, 20702, 20902, 21112, 21512, 21712, 22322, 22522, 23332, 23732, 24142

Offset

1,1

Comments

a(1)=212, 212 is palindromic number, sum of digits 5 is prime, number of prime digits {2,2} 2 is prime, a(10)=575, 575 is palindromic number, sum of digits 17 is prime, number of prime digits {5,5,7} 3 is prime, a(15)=12121, 12121 is palindromic number, sum of digits 7 is prime, number of prime digits {2,2} 2 is prime, ...

Links

Table of n, a(n) for n=1..38.

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; ans1:=[ op(ans1), op(i, ans) ]: fi od; RETURN(stpf) end: # Return 0, if palindrome, otherwise return 1 ts_numpal:=proc(n) local ad; ad:=convert(n, base, 10): if (ListTools[Reverse](ad)=ad) then return 0; else return 1; fi end: # Return sum of digits ts_vsota_stevk:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do stpf:=stpf+op(i, ans); od; RETURN(stpf) end: ts_pras_vsota_pra_stevk_palind:=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' and ts_numpal(i)=0) then ans:=[ op(ans), i ]: fi od; RETURN(ans) end: ts_pras_vsota_pra_stevk_palind(100000);

Crossrefs

Sequence in context: A099687 A358873 A133651 * A088642 A251126 A078211

Adjacent sequences: A093804 A093805 A093806 * A093808 A093809 A093810

Keyword

nonn,base

Author

Jani Melik, May 19 2004

Status

approved