

A344366


Integers k such that the sum of squares of digits of both k and k1 are prime.


0



12, 102, 111, 120, 160, 230, 250, 380, 410, 450, 520, 560, 720, 780, 830, 870, 1002, 1011, 1020, 1060, 1100, 1101, 1110, 1370, 1640, 1680, 1910, 1950, 1970, 1990, 2030, 2050, 2340, 2670, 2920, 3080, 3170, 3240, 3420, 3460, 3550, 3570, 3710, 3840, 3860, 4010
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OFFSET

1,1


COMMENTS

Integers k such that k and k1 are both in A108662.
Terms are never prime. They cannot end in the digits 3,4,5,6,7,8,9.
If k is a term, phi(k) is divisible by 4.
The set of such numbers is infinite.


LINKS

Table of n, a(n) for n=1..46.
Charles U. Lonappan, Consecutive natural numbers whose sum of squares of digits is prime, International Journal of Research in Engineering and Science (IJRES), Volume 9 Issue 1 (2021) pp. 1416.


EXAMPLE

12 is in the sequence because the sum of squares of digits of 12 is 5 and that of 11 is 2, and both 5 and 2 are prime numbers.


MATHEMATICA

q[n_] := PrimeQ[Plus @@ (IntegerDigits[n]^2)]; Select[Range[2, 5000], q[#1] && q[#] &] (* Amiram Eldar, May 19 2021 *)


PROG

(PARI) isok(k) = isprime(norml2(digits(k1))) && isprime(norml2(digits(k))); \\ Michel Marcus, May 24 2021


CROSSREFS

Cf. A108662.
Sequence in context: A008547 A109020 A099299 * A304504 A344279 A022736
Adjacent sequences: A344363 A344364 A344365 * A344367 A344368 A344369


KEYWORD

nonn,base


AUTHOR

Charles U. Lonappan, May 19 2021


STATUS

approved



