

A275971


Numbers n such that the decimal digits of n^2 are all prime.


4



5, 15, 85, 165, 235, 485, 1665, 1885, 4835, 5765, 7585, 15085, 15885, 16665, 18365, 18915, 22885, 27115, 27885, 50235, 57665, 58115, 72335, 85635, 87885, 150915, 166665, 182415, 194235, 194365, 229635, 240365, 268835, 503515, 507665, 524915, 568835, 570415, 577515, 581165
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OFFSET

1,1


COMMENTS

Apparently 5, 235 and 72335 are the only terms using digits {2,3,5,7}.
a(n)/5 = {1, 3, 17, 33, 47, 97, 333, 377, 967, 1153, 1517, 3017, 3177, 3333, ...}; terms b(n) that have n 3's must be in the sequence since (5 b(n))^2 yields the decimal number 2 followed by (n1) 7's then n 2's, and ending in 5 (i.e., 225, 27225, 2772225). Thus 5 b(n) = {15, 165, 1665, 16665, etc.} appears in this sequence.  Michael De Vlieger, Aug 15 2016
All terms are odd multiples of 5 (A017329), i.e., must end in 5, which is the only digit whose square ends in a prime digit. The sequence contains A030487 as an infinite proper subsequence which in turn contains all numbers of the form (5*10^n5)/3 (these are the above 5 b(n)) as a proper subsequence.  M. F. Hasler, Sep 16 2016


LINKS

Michel Marcus, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = sqrt(A191486(n)).


EXAMPLE

72335^2 = 5232352225 = A191486(23).


MATHEMATICA

w = Boole@! PrimeQ@ # & /@ RotateLeft@ Range[0, 9]; Sqrt@ Select[Range[10^6]^2, Total@ Pick[DigitCount@ #, w, 1] == 0 &] (* Michael De Vlieger, Aug 15 2016 *)


PROG

(PARI) is(n)=#setintersect(Set(digits(n^2)), [0, 1, 4, 6, 8, 9])==0 \\ Charles R Greathouse IV, Sep 16 2016


CROSSREFS

Cf. A191486, A017329, A030487.
Sequence in context: A064678 A088935 A183937 * A030487 A165470 A165625
Adjacent sequences: A275968 A275969 A275970 * A275972 A275973 A275974


KEYWORD

nonn,base


AUTHOR

Zak Seidov, Aug 15 2016


EXTENSIONS

More terms from Michel Marcus, Aug 17 2016


STATUS

approved



