A253848 - OEIS

%I #12 Sep 07 2015 14:45:28

%S 43,61,151,197,199,397,601,661,733,823,883,1051,1093,1123,1297,1381,

%T 1453,1471,1543,1831,1873,2281,2371,2551,2683,2713,2953,2971,3181,

%U 3343,3361,3583,3613,3631,4003,4153,4261,4513,4603,4621,4801,4951,5011,5101,5323,5413

%N Primes p such that the digit sums of p, p + 4 and p^2 + 4 are all prime.

%H K. D. Bajpai, <a href="/A253848/b253848.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 43: 43+4 = 47; 43^2+4 = 1853. Their digit sums 4+3 = 7, 4+7 = 11 and 1+8+5+3 = 17 are all prime.

%e a(2) = 61: 61+4 = 65; 61^2+4 = 3725. Their digit sums 6+1 = 7, 6+5 = 11 and 3+7+2+5 = 17 are all prime.

%p digsum:= n -> convert(convert(n,base,10),`+`):

%p select(p -> isprime(p) and isprime(digsum(p)) and isprime(digsum(p+4)) and isprime(digsum(p^2+4)), [2,seq(2*k+1, k=1..10^4)]); # _Robert Israel_, Jan 16 2015

%t k = 4; Select[Prime[Range[1, 2000]], PrimeQ[Plus @@ IntegerDigits[#]] && PrimeQ[Plus @@ IntegerDigits[k+#]] && PrimeQ[Plus @@ IntegerDigits[k+#^2]] &]

%t Select[Prime[Range[800]],AllTrue[Total/@IntegerDigits[{#,#+4,#^2+4}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 14 2015 *)

%o (PARI) for( n=1, 10^2, p=prime(n);  k=4; if(isprime(eval(Str(sumdigits(p)))) & isprime(eval(Str(sumdigits(p+k)))) &isprime(eval(Str(sumdigits(p^2+k)))), print1(p,"  ",) ) )

%o (PARI) forprime(p=1,10000,if(isprime(sumdigits(p)) && isprime(sumdigits(p+4)) && isprime(sumdigits(p^2+4)),print1(p", "))) \\ _Dana Jacobsen_, Sep 07 2015

%o (Perl) use ntheory ":all"; forprimes { say if is_prime(sumdigits($_)) && is_prime(sumdigits($_+4)) && is_prime(sumdigits($_*$_+4)) } 1000; # _Dana Jacobsen_, Sep 07 2015

%Y Cf. A000040, A076162, A243586.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jan 16 2015