A307046 Numbers k such that k^2 reversed is a prime and k^2 + (k^2 reversed) is a semiprime.
4, 28, 40, 62, 106, 140, 193, 196, 274, 316, 334, 400, 410, 554, 556, 620, 862, 866, 874, 884, 962, 1004, 1025, 1066, 1154, 1174, 1190, 1205, 1256, 1274, 1294, 1360, 1390, 1394, 1396, 1400, 1744, 1784, 1816, 1844, 1891, 1900, 1927, 1960, 1981, 1988, 2672, 2696, 2710, 2722, 2740, 2786, 2800, 3016, 3026
Offset: 1
Examples
4^2=16, reversed is 61. 16+61=77 which is semiprime (7*11), so 4 is in this sequence.
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(n) local a,b; a:= n^2; b:= revdigs(a); isprime(b) and numtheory:-bigomega(a+b)=2 end proc: select(filter, [$1..10000]); # Robert Israel, Mar 31 2019
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Mathematica
Select[Range[50000], PrimeQ[IntegerReverse[#^2]] && PrimeOmega[#^2 + IntegerReverse[#^2]] == 2 &]