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Semiprimes whose reversal + 1 is a square.
1

%I #13 Jun 25 2022 12:02:05

%S 51,323,341,422,591,993,998,4227,4265,5129,5534,5921,5937,8049,8657,

%T 8801,9953,32133,32282,32471,32597,32817,34091,34379,36611,36863,

%U 38937,42011,42243,42605,53211,53673,55745,57167,57903,59543,82151,86354,86781,88217,88433

%N Semiprimes whose reversal + 1 is a square.

%C Semiprimes in A245361.

%C Similar sequence for primes at A167217.

%H K. D. Bajpai, <a href="/A245362/b245362.txt">Table of n, a(n) for n = 1..1054</a>

%e 341 is in the sequence because 341 = 11 * 31, which is semiprime, and reversal(341) + 1 = 143 + 1 = 144 = 12^2.

%e 591 is in the sequence because 591 = 3 * 197, which is semiprime, and reversal(591) + 1 = 195 + 1 = 196 = 14^2.

%t Select[Range[10^5], PrimeOmega[#] == 2 && IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[#]]] + 1]] &]

%o (PARI)

%o revint(n) = eval(concat(Vecrev(Str(n))))

%o select(n->bigomega(n)==2 && issquare(revint(n)+1), vector(100000, n, n)) \\ _Colin Barker_, Jul 20 2014

%Y Cf. A000290, A001358, A167217, A245361.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jul 18 2014