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A344825
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Integers whose digit sum is prime and whose digit product is a perfect square > 0.
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2
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11, 14, 41, 49, 94, 111, 119, 122, 128, 133, 155, 166, 182, 188, 191, 199, 212, 218, 221, 229, 236, 263, 281, 289, 292, 298, 313, 326, 331, 362, 368, 386, 449, 494, 515, 551, 559, 595, 616, 623, 632, 638, 661, 683, 779, 797, 812, 818, 821, 829, 836, 863, 881
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OFFSET
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1,1
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COMMENTS
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If k is in the sequence then all anagrams of k are in the sequence. - David A. Corneth, May 29 2021
Trivially, this sequence has infinite elements. A031974 is an infinite sequence that is found in this sequence - Ryan Bresler, May 30 2021
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LINKS
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EXAMPLE
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11 is a term because its digit sum is 2 (prime) and its digit product is 1 (perfect square > 0).
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MAPLE
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q:= n-> (l-> not 0 in l and isprime(add(i, i=l)) and
issqr(mul(i, i=l)))(convert(n, base, 10)):
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PROG
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(Python)
from math import prod
from sympy import isprime, integer_nthroot
def ok(n):
d = list(map(int, str(n)))
return 0 not in d and isprime(sum(d)) and integer_nthroot(prod(d), 2)[1]
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CROSSREFS
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A031974 is a subsequence of this sequence.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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