A093808 Palindromic primes with property that sum of digits is prime and number of prime digits is prime.

313, 353, 373, 757, 797, 12721, 13331, 13931, 15551, 30103, 30703, 31513, 32323, 33533, 34543, 35353, 35753, 36563, 38183, 38783, 70507, 71317, 74747, 75557, 76367, 77377, 78787, 79997, 93739, 95959, 97579

Offset

1,1

Comments

There are just 31 such numbers below 10^5.

Links

Table of n, a(n) for n=1..31.

Example

a(1)=313, 313 is palindromic prime, sum of digits 7 is prime, number of prime digits {3,3} 2 is prime,
a(8)13931, 13931 is palindromic prime, sum of digits 17 is prime, number of prime digits {3,3} 2 is prime,
a(11)=30703, 30703 is palindromic prime, sum of digits 17 is prime, number of prime digits {3,3,7} 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; 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_pras:=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 isprime(i)='true' and ts_numpal(i)=0) then ans:=[ op(ans), i ]: fi od; RETURN(ans) end: ts_pras_vsota_pra_stevk_palind_pras(1000000);

Crossrefs

Sequence in context: A082584 A088282 A068687 * A257527 A142745 A328056

Adjacent sequences: A093805 A093806 A093807 * A093809 A093810 A093811

Keyword

nonn,base

Author

Jani Melik, May 19 2004

Status

approved