A065073 -id:A065073 - cp's OEIS frontend

A007605 Sum of digits of n-th prime.

2, 3, 5, 7, 2, 4, 8, 10, 5, 11, 4, 10, 5, 7, 11, 8, 14, 7, 13, 8, 10, 16, 11, 17, 16, 2, 4, 8, 10, 5, 10, 5, 11, 13, 14, 7, 13, 10, 14, 11, 17, 10, 11, 13, 17, 19, 4, 7, 11, 13, 8, 14, 7, 8, 14, 11, 17, 10, 16, 11, 13, 14, 10, 5, 7, 11, 7, 13, 14, 16, 11, 17, 16, 13, 19, 14, 20, 19, 5

Offset: 1

N. J. A. Sloane, Mira Bernstein, and Robert G. Wilson v

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
CNRS press release, Sum of Digits of Prime Numbers Is Evenly Distributed: New Mathematical Proof of Hypothesis
Christian Mauduit and Joël Rivat, Sur un problème de Gelfond: la somme des chiffres des nombres premiers (French) [On a problem posed by Gelfond: the sum of digits of primes] Ann. of Math. (2) 171(2010), no. 3, 1591--1646. MR2680394 (2011j:11137)
Enrique Navarrete, Distributions of Sums of Digits of Primes
Robert G. Wilson v, Letter to C. A. Pickover, Mar. 1993

Cf. A000040, A007953, A038194, A065073, A068395, A133223, A376714, A380192.

For inverse, see A067180 and A067523.

a007605_list = map a007953 a000040_list -- Reinhard Zumkeller, Aug 04 2011

[ &+Intseq(NthPrime(n), 10): n in [1..80] ]; // Klaus Brockhaus, Jun 13 2009

map(t -> convert(convert(t,base,10),`+`), select(isprime, [2,(2*i+1 $ i=1..1000)])); # Robert Israel, Aug 16 2015

Table[Apply[Plus, RealDigits[Prime[n]][[1]]], {n, 1, 100}]
Plus@@ IntegerDigits[Prime[Range[100]]] (* Zak Seidov *)

dsum(n)=my(s);while(n,s+=n%10;n\=10);s
forprime(p=2,1e3,print1(dsum(p)", ")) \\ Charles R Greathouse IV, Jul 15 2011

a(n) = sumdigits(prime(n)); \\ Michel Marcus, Dec 20 2017

from sympy import prime
def a(n): return sum(map(int, str(prime(n))))
print([a(n) for n in range(1, 80)]) # Michael S. Branicky, Feb 03 2021

a(n) = A007953(A000040(n)) = A007953(prime(n)).

A048519 Prime plus its digit sum equals a prime.

Original entry on oeis.org

11, 13, 19, 37, 53, 59, 71, 73, 97, 101, 103, 127, 149, 163, 167, 181, 233, 257, 271, 277, 293, 307, 367, 383, 389, 419, 431, 433, 479, 499, 509, 547, 563, 587, 617, 631, 701, 727, 743, 787, 811, 839, 857, 859, 947, 1009, 1049, 1061, 1087, 1153, 1171

Offset: 1

Patrick De Geest, May 15 1999

For any prime p, p +- digitsum(p, base b) can't be prime unless the base b is even, since in an odd base, an odd number always has an odd digit sum (powers of b are congruent to b (mod 2)), so p +- digitsum(p, base b) is even for odd b. This sequence is for b = 10 (where "-" is also excluded, see comment in A243442), see A243441 for b = 2. - M. F. Hasler, Nov 06 2018

See subsequence A048523 for primes which only once give another prime under iteration of A062028, and A048524 .. A048527, A320878 .. A320880 for primes starting longer chains. See A090009 for their initial terms, starting the earliest chain of given length. - M. F. Hasler, Nov 09 2018

			a(9) = prime 97 because 97 + sum-of-digits(97) = 97 + 16 = 113 also a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A007953 (digit sum), A062028 (n + digit sum of n), A047791 (A062028(n) is prime), A048520.
Cf. A006378, A107740.
Cf. A000040, A010051, A065073.
Cf. A048523 .. A048527, A320878, A320879, A320880, A090009.

a048519 n = a048519_list !! (n-1)
a048519_list = map a000040 $ filter ((== 1) . a010051' . a065073) [1..]
-- Reinhard Zumkeller, Sep 27 2014

[p: p in PrimesUpTo(1200) | IsPrime(q) where q is p+&+Intseq(p)]; // Vincenzo Librandi, Jan 30 2018

select(n -> isprime(n) and isprime(n + convert(convert(n,base,10),`+`)), [$1..10^4]); # Robert Israel, Aug 10 2014

Select[Prime[Range[500]],PrimeQ[#+Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Oct 03 2011 *)

select( is(p)=isprime(p+sumdigits(p))&&isprime(p), primes([0,2000])) \\ M. F. Hasler, Aug 08 2014, edited Nov 09 2018

Primes in A047791, i.e., intersection of A047791 and A000040. - M. F. Hasler, Nov 08 2018

A068395 a(n) = n-th prime minus its sum of digits.

Original entry on oeis.org

0, 0, 0, 0, 9, 9, 9, 9, 18, 18, 27, 27, 36, 36, 36, 45, 45, 54, 54, 63, 63, 63, 72, 72, 81, 99, 99, 99, 99, 108, 117, 126, 126, 126, 135, 144, 144, 153, 153, 162, 162, 171, 180, 180, 180, 180, 207, 216, 216, 216, 225, 225, 234, 243, 243, 252, 252, 261, 261, 270

Offset: 1

Reinhard Zumkeller, Mar 08 2002

a(i) <= a(j) for i < j.
A number and the sum of its digits have the same value modulo 9. Hence all terms are divisible by 9. - Stefan Steinerberger, Apr 01 2006
A192977 gives number of occurrences of multiples of 9. - Reinhard Zumkeller, Aug 04 2011
Margaret Coffey (ed.) p. 440: "The sum of the digits of a two-digit prime number is subtracted from the number.  Prove that the difference cannot be a prime number."  Proof [p.442] "Let a and b be the tens and units digits, respectively, and let 10a+b be the prime.  Subtract the sum of the digits from the number: 10a + b - (a+b) = 9a.  The difference is a multiple of 9 and cannot, therefore, be prime." - Jonathan Vos Post, Feb 02 2012

			a(10) = 29 - (2+9) = 18.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Margaret Coffey, Editor, Problem #3, Calendar, Mathematics Teacher, March 2012, pp. 440-442.

Cf. A065073.

a068395 n = a068395_list !! (n-1)
a068395_list = zipWith (-) a000040_list a007605_list
-- Reinhard Zumkeller, Aug 04 2011

Table[Prime[n] - Sum[DigitCount[Prime[n]][[i]]*i, {i, 1, 9}], {n, 1, 60}] (* Stefan Steinerberger, Apr 01 2006 *)
#-Total[IntegerDigits[#]]&/@Prime[Range[60]] (* Harvey P. Dale, Oct 14 2014 *)

a(n) = A000040(n) - A007953(A000040(n)).

More terms from Stefan Steinerberger, Apr 01 2006

A184328 Primes whose digital product is a positive square.

Original entry on oeis.org

11, 19, 41, 149, 191, 199, 229, 263, 281, 313, 331, 419, 433, 449, 491, 499, 661, 683, 797, 821, 829, 863, 881, 911, 919, 941, 977, 991, 1229, 1289, 1433, 1499, 1559, 1669, 1747, 1889, 1933, 1949, 1999, 2129, 2383, 2693, 2819, 2833, 2963, 3319, 3391, 3413

Offset: 1

Dario Piazzalunga, Dec 24 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A053666, A007954, A007605, A065073, A068395.

[p: p in PrimesUpTo(4000) | not IsZero(t) and IsSquare(t) where t is &*Intseq(p)]; // Bruno Berselli, Dec 25 2012

fQ[n_] := Module[{d = Times @@ IntegerDigits[n]}, d > 0 && IntegerQ[Sqrt[d]]];Select[Prime[Range[1000]], fQ] (* T. D. Noe, Dec 24 2012 *)

Corrected and extended by T. D. Noe, Dec 24 2012

cp's OEIS Frontend

A007605 Sum of digits of n-th prime.

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A048519 Prime plus its digit sum equals a prime.

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A068395 a(n) = n-th prime minus its sum of digits.

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A184328 Primes whose digital product is a positive square.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Extensions