A093807 - OEIS

%I #12 Jul 26 2024 20:21:15

%S 212,232,272,292,313,353,373,515,535,575,595,737,757,797,12121,12521,

%T 12721,13331,13531,13931,15151,15551,15751,17171,17371,17771,20102,

%U 20302,20702,20902,21112,21512,21712,22322,22522,23332,23732,24142

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

%C 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, ...

%H Michael S. Branicky, <a href="/A093807/b093807.txt">Table of n, a(n) for n = 1..10000</a>

%p # 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);

%t Cases[If[PalindromeQ@#,{#, {Count[IntegerDigits@#, _?PrimeQ], DigitSum@#}}, Nothing] & /@ Range@60000, {a_, {_?PrimeQ ..}} :>a] (* _Hans Rudolf Widmer_, Jul 26 2024 *)

%o (Python)

%o from sympy import isprime, nextprime

%o from itertools import count, islice, product

%o def pals(d): # all d-digit palindromes with odd middle digit, as strings

%o     for p in product("0123456789", repeat=d//2):

%o         if d//2 > 0 and p[0] == "0": continue

%o         left = "".join(p); right = left[::-1]

%o         for mid in [[""], "13579"][d%2]: yield left + mid + right

%o def agen(): # generator of terms

%o     for d in count(3, 2):

%o         yield from (int(p) for p in pals(d) if isprime(sum(1 for s in p if s in "2357")) and isprime(sum(map(int, p))))

%o print(list(islice(agen(), 38))) # _Michael S. Branicky_, Jul 26 2024

%K nonn,base

%O 1,1

%A _Jani Melik_, May 19 2004