A254038 Prime numbers n such that replacing each digit d in the decimal expansion of n with prime(d) produces a square. Zeros are not allowed.

13, 113, 6113, 33113, 93113, 123113, 18237113, 644312113, 749676113, 1222457113, 1346384113, 2343264113, 3282836113, 3959424113, 4412442113, 6241338113, 8932217113, 9165131113, 12165131113, 14198291113, 16224432113, 26199212113, 31259424113, 38785631113, 39232638113

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, ...

Links

Table of n, a(n) for n=1..25.

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

Sequence in context: A089569 A048383 A230377 * A221369 A320213 A323037

Adjacent sequences: A254035 A254036 A254037 * A254039 A254040 A254041

Keyword

nonn,base

Author

Michel Lagneau, Jan 23 2015

Status

approved