A253848 Primes p such that the digit sums of p, p + 4 and p^2 + 4 are all prime.

43, 61, 151, 197, 199, 397, 601, 661, 733, 823, 883, 1051, 1093, 1123, 1297, 1381, 1453, 1471, 1543, 1831, 1873, 2281, 2371, 2551, 2683, 2713, 2953, 2971, 3181, 3343, 3361, 3583, 3613, 3631, 4003, 4153, 4261, 4513, 4603, 4621, 4801, 4951, 5011, 5101, 5323, 5413

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

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.
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.

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A076162, A243586.

Sequence in context: A063641 A129928 A317393 * A245742 A295702 A102269

Adjacent sequences: A253845 A253846 A253847 * A253849 A253850 A253851

Keyword

nonn,base

Author

K. D. Bajpai, Jan 16 2015

Status

approved