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

1,1

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.

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. 14-16.

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(k-1))) && 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