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A006378
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Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum.
(Formerly M2427)
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17
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3, 5, 7, 31, 53, 97, 211, 233, 277, 367, 389, 457, 479, 547, 569, 613, 659, 727, 839, 883, 929, 1021, 1087, 1109, 1223, 1289, 1447, 1559, 1627, 1693, 1783, 1873, 2099, 2213, 2347, 2437, 2459, 2503, 2549, 2593, 2617, 2683, 2729, 2819, 2953, 3023, 3067
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 116.
D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.
D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.
D. R. Kaprekar, The Mathematics of the New Self Numbers (Part V). 311 Devlali Camp, Devlali, India, 1967.
Jeffrey Shallit, personal communication c. 1999.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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B. Recamán, Problem E2408, Amer. Math. Monthly, 81 (1974), p. 407.
T. Trotter, Charlene Numbers (Copy as of Jan. 2018 on web.archive.org; original page no longer available.) Originally published Nov. 2010.
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FORMULA
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MATHEMATICA
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With[{nn=3200}, Complement[Prime[Range[PrimePi[nn]]], Table[n+Total[ IntegerDigits[n]], {n, nn}]]] (* Harvey P. Dale, Dec 30 2011 *)
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PROG
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(Haskell)
a006378 n = a006378_list !! (n-1)
a006378_list = map a000040 $ filter ((== 0) . a107740) [1..]
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CROSSREFS
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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STATUS
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approved
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