A290972 Primes p such that the sum of the squares of digits of p equals the sum of digits of p^2.

2, 3, 3331, 3433, 11243, 13241, 21523, 22153, 22531, 31541, 32141, 32411, 33203, 34033, 34141, 34211, 35141, 41341, 41413, 42131, 43411, 44131, 51341, 51413, 52321, 54311, 102253, 102523, 104231, 104513, 110543, 111263, 111623, 112163

Offset: 1

Author

K. D. Bajpai, Aug 16 2017

Keywords

• nonn
• base

Comments

214007 is the smallest term that is in A017353 and 31111009 is the smallest term that is in A017377. - Altug Alkan, Aug 16 2017

Examples

			a(3) = 3331 is prime: [3^2 + 3^2 + 3^2 + 1^2 = 9 + 9 + 9 + 1] = 28; [3331^2 = 11095561, 1 + 1 + 0 + 9 + 5 + 5 + 1] = 28.
a(5) = 11243 is prime: [1^2 + 1^2 + 2^2 + 4^2 + 3^2 = 1 + 1 + 4 + 16 + 9] = 31: [11243^2 = 126405049;1 + 2 + 6 + 4 + 0 + 5 + 0 + 4 + 9] = 31.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Intersection of A000040 and A165550.

Cf. A123157.

Programs

Maple

filter:= t -> convert(map(`^`,convert(t,base,10),2),`+`) = convert(convert(t^2,base,10),`+`) and isprime(t):
select(filter, [2,seq(i,i=3..200000,2)]); # Robert Israel, Aug 16 2017

Mathematica

Select[Prime[Range[20000]], Plus @@ IntegerDigits[#^2] == Total[IntegerDigits[#]^2] &]

PARI

forprime(p=1, 30000, v=digits(p); if(sum(i=1, length(v), v[i]^2) == sumdigits(p^2), print1(p", ")));