A344045 Primes p such that the decimal digits of p^2 can be partitioned into two or more squares.

7, 13, 19, 37, 41, 97, 107, 191, 223, 379, 397, 487, 509, 701, 997, 1049, 1063, 1093, 1201, 1301, 1801, 1907, 2011, 2029, 3019, 3169, 3319, 3371, 3767, 4013, 4451, 5009, 5011, 5081, 5099, 5693, 6037, 6397, 7001, 8009, 9041, 9521, 9619, 9721, 9907, 10007

Offset

1,1

Comments

Similar to A048646 except that here zeros are permitted as squares.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..200

Example

97 is a term because 97 is a prime and 97^2 = 9409 which can be partitioned into 9, 4, 0, and 9, each of which is a square.

Mathematica

tmsQ[n_]:=Total[Boole[AllTrue[Sqrt[#], IntegerQ]&/@Rest[Table[FromDigits/@ TakeList[IntegerDigits[n^2], q], {q, Flatten[Permutations/@ IntegerPartitions[ IntegerLength[ n^2]], 1]}]]]]>0; Select[Prime[ Range[ 3000]], tmsQ]

Crossrefs

Cf. A048646, A048653, A128783.

Sequence in context: A208776 A108295 A071923 * A048646 A152087 A098059

Adjacent sequences: A344042 A344043 A344044 * A344046 A344047 A344048

Keyword

nonn,base

Author

Harvey P. Dale, May 09 2021

Status

approved