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A062339 Primes whose sum of digits is 4. 26
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.
FORMULA
Intersection of A052218 (digit sum 4) and A000040 (primes). - M. F. Hasler, Mar 09 2022
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
From M. F. Hasler, Mar 09 2022: (Start)
(PARI) select( {is_A062339(p, s=4)=sumdigits(p)==s&&isprime(p)}, primes([1, 10^7])) \\ 2nd optional parameter for similar sequences with other digit sums
(PARI) {A062339_upto_length(L, s=4, a=List(), u=[10^(L-k)|k<-[1..L]])=forvec(d=[[1, L]|i<-[1..s]], isprime(p=vecsum(vecextract(u, d))) && listput(a, p), 1); Vecrev(a)} \\ (End)
(Magma) [p: p in PrimesUpTo(800000000) | &+Intseq(p) eq 4]; // Vincenzo Librandi, Jul 08 2014
CROSSREFS
Cf. A000040 (primes), A052218 (digit sum = 4), A061239 (primes == 4 (mod 9)).
Cf. Primes p with digital sum equal to k: {2, 11 and 101} for k=2; this sequence (k=4), A062341 (k=5), A062337 (k=7), A062343 (k=8), A107579 (k=10), A106754 (k=11), A106755 (k=13), A106756 (k=14), A106757 (k=16), A106758 (k=17), A106759 (k=19), A106760 (k=20), A106761 (k=22), A106762 (k=23), A106763 (k=25), A106764 (k=26), A048517 (k=28), A106766 (k=29), A106767 (k=31), A106768 (k=32), A106769 (k=34), A106770 (k=35), A106771 (k=37), A106772 (k=38), A106773 (k=40), A106774 (k=41), A106775 (k=43), A106776 (k=44), A106777 (k=46), A106778 (k=47), A106779 (k=49), A106780 (k=50), A106781 (k=52), A106782 (k=53), A106783 (k=55), A106784 (k=56), A106785 (k=58), A106786 (k=59), A106787 (k=61), A107617 (k=62), A107618 (k=64), A107619 (k=65), A106807 (k=67), A244918 (k=68), A181321 (k=70).
Cf. A049054 (10^k+3 is prime), A159352 (these primes).
Cf. A056807 (3*10^k+1 is prime), A259866 (these primes).
Subsequence of A107715 (primes with digits <= 3).
Cf. A020449 (primes with digits 0 and 1), A036953 (primes with digits <= 2), A106100 (primes with largest digit = 2), A069663, A069664 (smallest resp. largest n-digit prime with minimum digit sum).
Sequence in context: A160772 A271575 A039403 * A368051 A043226 A044006
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 March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)