A344366 Integers k such that the sum of squares of digits of both k and k-1 are prime.

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

Offset: 1

Author

Charles U. Lonappan, May 19 2021

Keywords

• nonn
• base

Comments

Integers k such that k and k-1 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.

Examples

			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.
		

Links

• 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. 14-16.

Crossrefs

Cf. A108662.

Programs

Mathematica

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

PARI

isok(k) = isprime(norml2(digits(k-1))) && isprime(norml2(digits(k))); \\ Michel Marcus, May 24 2021