%I M2427 #60 Apr 07 2022 10:44:33

%S 3,5,7,31,53,97,211,233,277,367,389,457,479,547,569,613,659,727,839,

%T 883,929,1021,1087,1109,1223,1289,1447,1559,1627,1693,1783,1873,2099,

%U 2213,2347,2437,2459,2503,2549,2593,2617,2683,2729,2819,2953,3023,3067

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

%D M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 116.

%D D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.

%D D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.

%D D. R. Kaprekar, The Mathematics of the New Self Numbers (Part V). 311 Devlali Camp, Devlali, India, 1967.

%D Jeffrey Shallit, personal communication c. 1999.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Donovan Johnson, <a href="/A006378/b006378.txt">Table of n, a(n) for n = 1..10000</a>

%H Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

%H D. R. Kaprekar, <a href="/A003052/a003052_2.pdf">The Mathematics of the New Self Numbers</a> [annotated and scanned]

%H B. Recamán, <a href="http://www.jstor.org/stable/2319017">Problem E2408</a>, Amer. Math. Monthly, 81 (1974), p. 407.

%H T. Trotter, <a href="http://web.archive.org/http://trottermath.net/charlene-numbers/">Charlene Numbers</a> (Copy as of Jan. 2018 on web.archive.org; original page no longer available.) Originally published Nov. 2010.

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%F A107740(A049084(a(n))) = 0. [Corrected by _Reinhard Zumkeller_, Sep 27 2014]

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

%o (Haskell)

%o a006378 n = a006378_list !! (n-1)

%o a006378_list = map a000040 $ filter ((== 0) . a107740) [1..]

%o -- _Reinhard Zumkeller_, Sep 27 2014

%o (PARI) select( is_A006378(n)=is_A003052(n)&&isprime(n), primes([1,3000])) \\ _M. F. Hasler_, Nov 08 2018

%Y Subsequence of A247104.

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

%K nonn,base,nice,easy

%O 1,1

%A _N. J. A. Sloane_