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%I #57 Jun 07 2021 10:28:18
%S 12,102,111,120,160,230,250,380,410,450,520,560,720,780,830,870,1002,
%T 1011,1020,1060,1100,1101,1110,1370,1640,1680,1910,1950,1970,1990,
%U 2030,2050,2340,2670,2920,3080,3170,3240,3420,3460,3550,3570,3710,3840,3860,4010
%N Integers k such that the sum of squares of digits of both k and k-1 are prime.
%C Integers k such that k and k-1 are both in A108662.
%C Terms are never prime. They cannot end in the digits 3,4,5,6,7,8,9.
%C If k is a term, phi(k) is divisible by 4.
%C The set of such numbers is infinite.
%H Charles U. Lonappan, <a href="http://www.ijres.org/papers/Volume-9/Issue-1/D09011416.pdf">Consecutive natural numbers whose sum of squares of digits is prime</a>, International Journal of Research in Engineering and Science (IJRES), Volume 9 Issue 1 (2021) pp. 14-16.
%e 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.
%t q[n_] := PrimeQ[Plus @@ (IntegerDigits[n]^2)]; Select[Range[2, 5000], q[#-1] && q[#] &] (* _Amiram Eldar_, May 19 2021 *)
%o (PARI) isok(k) = isprime(norml2(digits(k-1))) && isprime(norml2(digits(k))); \\ _Michel Marcus_, May 24 2021
%Y Cf. A108662.
%K nonn,base
%O 1,1
%A _Charles U. Lonappan_, May 19 2021
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