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A062339
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Primes whose sum of digits is 4.
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26
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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Intersection of A052218 (digit sum 4) and A000040 (primes). - M. F. Hasler, Mar 09 2022
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EXAMPLE
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3001 is a prime with sum of digits = 4, hence belongs to the sequence.
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MAPLE
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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
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MATHEMATICA
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Union[FromDigits/@Select[Flatten[Table[Tuples[{0, 1, 2, 3}, k], {k, 9}], 1], PrimeQ[FromDigits[#]]&&Total[#]==4&]] (* Jayanta Basu, May 19 2013 *)
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PROG
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(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
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CROSSREFS
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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 * A043226 A044006 A179034
Adjacent sequences: A062336 A062337 A062338 * A062340 A062341 A062342
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KEYWORD
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nonn,base
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AUTHOR
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Amarnath Murthy, Jun 21 2001
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EXTENSIONS
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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
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STATUS
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approved
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