A306301 Numbers k such that k^2 reversed is a prime and k^2+(k^2 reversed) is a prime.
14, 136, 190, 266, 280, 1036, 1060, 1306, 1406, 1898, 1934, 2660, 2686, 2746, 2776, 3112, 10040, 10250, 10546, 10550, 10630, 10880, 11090, 11156, 11204, 11276, 11354, 11386, 11474, 11740, 11804, 11914, 12064, 12136, 12194, 12250, 12410, 12524, 12626, 12710, 12770, 12794, 12916, 13060
Offset: 1
Examples
14 is a term because 691 (the reverse of 14^2=196) and 196+691=887 are two prime numbers.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc: filter:= proc(k) local v; v:= revdigs(k^2); isprime(v) and isprime(v+k^2) end proc: select(filter, [seq(seq(6*i+j,j=[2,4]),i=0..10000)]); # Robert Israel, Apr 09 2019
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Mathematica
Select[Range[50000], PrimeQ[IntegerReverse[#^2]] && PrimeQ[#^2 + IntegerReverse[#^2]] &]
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PARI
isok(k) = my(kk=fromdigits(Vecrev(digits(k^2)))); isprime(kk) && isprime(k^2+kk); \\ Michel Marcus, Apr 01 2019
Comments