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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 * 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 March 24 15:55 EDT 2023. Contains 361479 sequences. (Running on oeis4.)