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A062339 Primes whose sum of digits is 4. 17
13, 31, 103, 211, 1021, 1201, 2011, 3001, 10111, 20011, 20101, 21001, 100003, 102001, 1000003, 1011001, 1020001, 1100101, 2100001, 10010101, 10100011, 20001001, 30000001, 101001001, 200001001, 1000000021, 1000001011, 1000010101, 1000020001, 1000200001, 1002000001, 1010000011 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a subsequence of A062338. Is this sequence (and its brothers A062337, A062341 and A062343) infinite?

10^A049054(m)+3 and 3*10^A056807(m)+1 are subsequences. A107715 (primes containing only digits from set {0,1,2,3}) is a supersequence. Terms not containing the digit 3 are either terms of A020449 (primes that contain digits 0 and 1 only) or of A106100 (primes with maximal digit 2) - and thus terms of these sequences' union A036953 (primes containing only digits from set {0,1,2}). - Rick L. Shepherd, May 23 2005

Subsequence of A107288. - Zak Seidov, Oct 29 2009

Includes A159352. - Robert Israel, Dec 28 2015

LINKS

T. D. Noe and Robert Israel, Table of n, a(n) for n = 1..10000 (n=1..1000 from T. D. Noe)

Amin Witno, Numbers which factor as their digital sum times a prime, International Journal of Open Problems in Computer Science and Mathematics 3:2 (2010), pp. 132-136.

EXAMPLE

3001 is a prime with sum of digits = 4, hence belongs to the sequence.

MAPLE

N:= 20: # to get all terms < 10^N

B[1]:= {1}:

B[2]:= {2}:

B[3]:= {3}:

A:= {}:

for d from 2 to N do

   B[4]:= map(t -> 10*t+1, B[3]) union  map(t -> 10*t+3, B[1]);

   B[3]:= map(t -> 10*t, B[3]) union map(t -> 10*t+1, B[2]) union map(t -> 10*t+2, B[1]);

   B[2]:= map(t -> 10*t, B[2]) union map(t -> 10*t+1, B[1]);

   B[1]:= map(t -> 10*t, B[1]);

   A:= A union select(isprime, B[4]);

od:

sort(convert(A, list)); # Robert Israel, Dec 28 2015

MATHEMATICA

Union[FromDigits/@Select[Flatten[Table[Tuples[{0, 1, 2, 3}, k], {k, 9}], 1], PrimeQ[FromDigits[#]]&&Total[#]==4&]] (* Jayanta Basu, May 19 2013 *)

PROG

(PARI) for(a=1, 20, for(b=0, a, for(c=0, b, if(isprime(k=10^a+10^b+10^c+1), print1(k", "))))) \\ Charles R Greathouse IV, Jul 26 2011

(MAGMA) [p: p in PrimesUpTo(800000000) | &+Intseq(p) eq 4]; // Vincenzo Librandi, Jul 08 2014

CROSSREFS

Cf. A062337, A062341, A062343, A049054, A056807, A107715, A020449, A106100, A036953, A069663, A069664, A159352

Cf. similar sequences listed in A244918.

Sequence in context: A160772 A271575 A039403 * A043226 A044006 A179034

Adjacent sequences:  A062336 A062337 A062338 * A062340 A062341 A062342

KEYWORD

nonn,base

AUTHOR

Amarnath Murthy, Jun 21 2001

EXTENSIONS

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 06 2001

More terms from Rick L. Shepherd, May 23 2005

More terms from Lekraj Beedassy, Dec 19 2007

STATUS

approved

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Last modified June 29 03:09 EDT 2017. Contains 288858 sequences.