A006378 Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum. (Formerly M2427)

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

Offset

1,1

References

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).

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]

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.

Index entries for Colombian or self numbers and related sequences

Formula

A107740(A049084(a(n))) = 0. [Corrected by Reinhard Zumkeller, Sep 27 2014]

Mathematica

With[{nn=3200}, Complement[Prime[Range[PrimePi[nn]]], Table[n+Total[ IntegerDigits[n]], {n, nn}]]] (* Harvey P. Dale, Dec 30 2011 *)

Prog

(Haskell)
a006378 n = a006378_list !! (n-1)
a006378_list = map a000040 $ filter ((== 0) . a107740) [1..]
-- Reinhard Zumkeller, Sep 27 2014
(PARI) select( is_A006378(n)=is_A003052(n)&&isprime(n), primes([1, 3000])) \\ M. F. Hasler, Nov 08 2018

Crossrefs

Subsequence of A247104.

Cf. A003052, A007953, A047791, A048521, A062028, A000040, A107740, A049084.

Sequence in context: A322749 A270269 A247104 * A162714 A359044 A002396

Adjacent sequences: A006375 A006376 A006377 * A006379 A006380 A006381

Keyword

nonn,base,nice,easy

Author

N. J. A. Sloane

Status

approved