A175964 Primes p such that each of the decimal numbers p^k for k=1..5 has exactly two 1s.

1217, 14591, 20611, 21481, 41941, 60161, 81371, 110533, 112223, 115099, 115237, 117053, 124133, 131939, 135841, 140551, 144139, 159013, 170123, 176819, 195731, 218521, 241051, 246511, 301241, 421241, 461561, 513001, 517261, 614143, 627511, 716819, 786151, 810149

Offset

1,1

Comments

Number of terms < 10^n: 0, 0, 0, 1, 7, 38, 266, ..., . - Robert G. Wilson v, Nov 05 2010

Links

Table of n, a(n) for n=1..34.

Example

1217^k with k=1..5: 1217, 1481089, 1802485313, 2193624625921, 2669641169745857.

Mathematica

fQ[n_] := DigitCount[{n, n^2, n^3, n^4, n^5}, 10, 1] == {2, 2, 2, 2, 2}; Select[ Prime@ Range@ 57800, fQ] (* Robert G. Wilson v, Nov 05 2010 *)
Select[Prime[Range[52000]], Union[DigitCount[#^Range[5], 10, 1]]=={2}&] (* Harvey P. Dale, Feb 18 2015 *)

Prog

(Python)
from somewhere import primegen
for p in primegen():
    if all(str(p**k).count('1') == 2 for k in range(1, 6)):
        print(p) # Lucas A. Brown, Mar 23 2024

Crossrefs

Sequence in context: A225759 A059669 A032628 * A300408 A252600 A293479

Adjacent sequences: A175961 A175962 A175963 * A175965 A175966 A175967

Keyword

base,nonn

Author

Zak Seidov, Oct 31 2010

Extensions

More terms from Robert G. Wilson v, Nov 05 2010

a(32)-a(34) from Lucas A. Brown, Mar 23 2024

Definition clarified by N. J. A. Sloane, Mar 23 2024

Status

approved