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A153631
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Numbers n such that n modulo (product of digits of n) = (sum of digits of n).
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1
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23, 29, 33, 39, 43, 49, 53, 59, 63, 69, 73, 79, 83, 89, 93, 99, 133, 136, 137, 192, 194, 195, 222, 223, 226, 229, 261, 263, 267, 313, 316, 331, 332, 333, 334, 336, 339, 391, 392, 397, 441, 443, 449, 621, 623, 661, 662, 663, 666, 669, 912, 914, 915, 931, 932
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OFFSET
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1,1
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COMMENTS
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Do consecutive numbers like 136, 137 occur frequently? Do many primes appear in the sequence?
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LINKS
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EXAMPLE
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For n = 83, (product of digits of n) = 24, (sum of digits of n) = 11 and 83 = 3*24 + 11.
For n = 93, (product of digits of n) = 27, (sum of digits of n) = 12 and 93 = 3*27 + 12.
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MAPLE
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sd := proc (n) options operator, arrow: add(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: pd := proc (n) options operator, arrow: product(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: a := proc (n) if 0 < pd(n) and `mod`(n, pd(n)) = sd(n) then n else end if end proc: seq(a(n), n = 1 .. 1000); # Emeric Deutsch, Jan 02 2009
A007953 := proc(n) local i ; add(i, i=convert(n, base, 10)) ; end: A007954 := proc(n) local i ; mul(i, i=convert(n, base, 10)) ; end: for n from 1 to 1200 do if A007954(n) > 0 then if irem(n, A007954(n))= A007953(n) then printf("%d, ", n) ; fi; fi; od: # R. J. Mathar, Jan 03 2009
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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Edited, corrected (93 inserted) and extended beyond a(21) by Klaus Brockhaus, Jan 06 2009
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STATUS
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approved
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