OFFSET
1,1
COMMENTS
a(1)==13(mod 100) and a(n)==113(mod 1000) for n>1.
The corresponding squares are 25, 225, 13225, 55225, 235225, 235225, 2193517225, 1377523225, 17723131713225, 233371117225, 257135197225, 35753137225, ...
EXAMPLE
6113 is in the sequence because 6113 becomes 13225 = 115^2, where 13225 is the concatenation (prime(6),prime(1),prime(1),prime(3))=(13,2,2,5).
MATHEMATICA
f[n_]:=Block[{a=IntegerDigits[n], b="", k=1, l}, l=Length[a]; While[k<l+1, b=StringJoin[b, ToString[Prime[a[[k]]]]]; k++]; ToExpression[b]]; Do[If[IntegerQ[Sqrt[f[Prime[n]]]], Print[Prime[n]]], {n, 1, 10^8}]
pnsQ[n_]:=Module[{c=FromDigits[Flatten[IntegerDigits/@Prime[ IntegerDigits[ n]]]]}, DigitCount[ c, 10, 0]==0&&IntegerQ[Sqrt[c]]]; Join[{13}, Select[ Range[113, 39232639000, 1000], PrimeQ[#]&&pnsQ[#]&]]//Quiet (* Harvey P. Dale, Apr 13 2019 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Jan 23 2015
STATUS
approved