A104211 -id:A104211 - cp's OEIS frontend

A028834 Numbers whose sum of digits is a prime.

2, 3, 5, 7, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 101, 102, 104, 106, 110, 111, 113, 115, 119, 120, 122, 124, 128, 131, 133, 137, 139, 140, 142, 146, 148, 151, 155, 157, 160, 164, 166, 173, 175, 179, 182

Offset: 1

Armand Turpel (armand(AT)vo.lu, armand_t(AT)geocities.com)

			89 included because 8+9 = 17, which is prime.

Christian N. K. Anderson, Table of n, a(n) for n = 1..25000 (terms 1..1000 from T. D. Noe)
Christian N. K. Anderson, Ulam Spiral for a(n) <= 100000.

Cf. A007953, A028835, A028842, A052018, A052019, A052020, A052021, A052022.
Cf. A010051; A046704 is a subsequence.
Complement of A104211.

a028834 n = a028834_list !! (n-1)
a028834_list = filter ((== 1) . a010051 . a007953) [1..]
-- Reinhard Zumkeller, Nov 13 2011

a:=proc(n) local nn: nn:=convert(n,base,10): if isprime(sum(nn[j],j=1..nops(nn)))=true then n else fi end: seq(a(n),n=1..200); # Emeric Deutsch, Mar 17 2007

Select[Range[200],PrimeQ[Total[IntegerDigits[#]]]&]  (* Harvey P. Dale, Feb 18 2011 *)

is(n)=isprime(sumdigits(n)) \\ Felix Fröhlich, Aug 16 2014

from sympy import isprime
def ok(n): return isprime(sum(map(int, str(n))))
print(list(filter(ok, range(183)))) # Michael S. Branicky, Jun 18 2021

require(gmp); which(sapply(1:1000, function(i) isprime(sum(floor(i/10^(0:(nchar(i)-1)))%%10)))==2) # Christian N. K. Anderson, Apr 22 2024

[x for x in range(200) if (sum(Integer(x).digits(base=10))) in Primes()] # Bruno Berselli, May 05 2014

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

A104213 Primes with nonprime sums of digits.

Original entry on oeis.org

13, 17, 19, 31, 37, 53, 59, 71, 73, 79, 97, 103, 107, 109, 127, 149, 163, 167, 181, 211, 233, 239, 251, 257, 271, 277, 293, 307, 347, 349, 367, 383, 389, 419, 431, 433, 439, 457, 479, 491, 499, 503, 509, 521, 523, 541, 547, 563, 569, 587, 613, 617, 619, 631

Offset: 1

Cino Hilliard, Mar 13 2005

Primes with nonprime digital sums. [Juri-Stepan Gerasimov, Apr 23 2010]

Subsequence of primes of A104211. - Michel Marcus, May 03 2015

			Sum of digits of prime 13 = 4, which is not prime, so 13 is in the sequence.

Jason Yuen, Table of n, a(n) for n = 1..10000

Cf. A046704 (primes with prime sums of digits), A104211.

[p: p in PrimesUpTo(600) | not IsPrime(&+Intseq(p))]; // Vincenzo Librandi, May 03 2015

Select[ Prime[ Range[115]], !PrimeQ[Plus @@ IntegerDigits[ # ]] &] (* Robert G. Wilson v, Mar 16 2005 *)

select(p->!isprime(sumdigits(p)),primes(100)) \\ Joerg Arndt, May 03 2015

Definition clarified by Jonathan Sondow, Jun 11 2012

A219110 Numbers for which at least one sum of two adjacent digits is not prime.

Original entry on oeis.org

10, 13, 15, 17, 18, 19, 22, 24, 26, 27, 28, 31, 33, 35, 36, 37, 39, 40, 42, 44, 45, 46, 48, 51, 53, 54, 55, 57, 59, 60, 62, 63, 64, 66, 68, 69, 71, 72, 73, 75, 77, 78, 79, 80, 81, 82, 84, 86, 87, 88, 90, 91, 93, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105

Offset: 1

M. F. Hasler, Apr 11 2013

Different from A104211 where ("only") the sum of all digits is considered; of course exactly the two-digit terms coincide.

Numbers missing in A182177 and A182178. Otherwise said, complement of the range of A182177 (in the set of nonnegative integers) and of the range of A182178 (in the set of positive integers) and of A182175 in the set of integers > 9.

			102 is here because 1+0 is not prime (even though 0+2 is).

M. F. Hasler in reply to E. Angelini, Re: Any digit-pair in S sums to a prime, SeqFan list, Apr 11 2013

Select[Range[10, 105], MemberQ[PrimeQ[Total /@ Partition[IntegerDigits[#], 2, 1]], False] &] (* T. D. Noe, Apr 16 2013 *)

is(n)=for(i=2,#n=digits(n),isprime(n[i-1]+n[i])||return(1))

A228019 Composite numbers whose sum of digits is a composite number.

Original entry on oeis.org

4, 6, 8, 9, 15, 18, 22, 24, 26, 27, 28, 33, 35, 36, 39, 40, 42, 44, 45, 46, 48, 51, 54, 55, 57, 60, 62, 63, 64, 66, 68, 69, 72, 75, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 91, 93, 95, 96, 99, 105, 108, 112, 114, 116, 117, 118, 121, 123, 125, 126, 129, 130, 132

Offset: 1

Derek Orr, Aug 02 2013

			87 is a term: 87 and 8+7=15 are composite.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Subsequence of A104211.

[n: n in [4..200] | not IsPrime(n) and not IsPrime(&+Intseq(n))]; // Bruno Berselli, Aug 13 2013

lista(N) = my(s); for(n=2,N, s=sumdigits(n); if(!isprime(n)&&!isprime(s)&&s>1, print1(n,", ") ) ) \\ Joerg Arndt, Aug 04 2013

list(N)=my(v=List(),s); forcomposite(n=4,N,s=sumdigits(n); if(s>1 && !isprime(s), listput(v,n))); Vec(v)  \\ Charles R Greathouse IV, Aug 13 2013

A154679 Primes p such that the sum of digits of p+2 is a composite number.

Original entry on oeis.org

2, 7, 11, 13, 17, 29, 31, 37, 43, 53, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 127, 139, 151, 157, 163, 167, 179, 181, 193, 211, 223, 229, 233, 241, 251, 257, 269, 271, 277, 283, 293, 307, 313, 331, 337, 347, 349, 359, 367, 373, 379, 383, 397, 409, 421, 431

Offset: 1

Giovanni Teofilatto, Jan 14 2009

Primes p such that p+2 is in A104211. [R. J. Mathar, Jan 15 2009]

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007953, A104211.

filter:= proc(n) local s;
if not isprime(n) then return false fi;
s:= convert(convert(n+2,base,10),`+`);
s >= 4 and not isprime(s)
end proc:
select(filter, [$2..1000]); # Robert Israel, Mar 13 2019

Select[Prime[Range[100]],CompositeQ[Total[IntegerDigits[#+2]]]&] (* Harvey P. Dale, Apr 28 2022 *)

Extended by R. J. Mathar, Jan 15 2009

A228020 Composite numbers whose initial, all intermediate and final iterated digit sums are composite numbers.

Original entry on oeis.org

4, 6, 8, 9, 15, 18, 22, 24, 26, 27, 33, 35, 36, 40, 42, 44, 45, 51, 54, 60, 62, 63, 69, 72, 78, 80, 81, 87, 90, 96, 99, 105, 108, 112, 114, 116, 117, 121, 123, 125, 126, 130, 132, 134, 135, 141, 143, 144, 150, 152, 153, 159, 161, 162, 168, 170, 171, 177, 180, 186, 189, 195, 198, 202, 204, 206

Offset: 1

Derek Orr, Aug 02 2013

a(n) is congruent to 0, 4, 6 or 8 mod 9. - Robert Israel, Aug 12 2014

			78 is a term because 78, 7+8 = 15, and 1+5 = 6 are composite.

Derek Orr, Table of n, a(n) for n = 1..10000

A subset of A228019 and A104211.

filter:= proc(n) local x;
x:= n;
do
   if isprime(x) then return false fi;
   if x < 10 then return (x > 1) fi;
   x:= convert(convert(x,base,10),`+`);
od:
end proc;
select(filter,[$4..1000]); # Robert Israel, Aug 12 2014

okQ[n_] := n > 1 && !PrimeQ[n] && (n < 10 || okQ@ Total@ IntegerDigits@ n); Select[Range@168, okQ] (* Giovanni Resta, Aug 05 2013 *)
cnQ[n_]:=AllTrue[NestWhileList[Total[IntegerDigits[#]]&,n,#>9&], CompositeQ]; Select[Range[210],cnQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 25 2016 *)

forcomposite(n=1,500,s=sumdigits(n);while(s>9&&!isprime(s)&&s!=1,s=sumdigits(s));if(!isprime(s)&&s!=1,print1(n,", "))) \\ Derek Orr, Aug 12 2014

A267430 Squares whose digit sum is not a prime.

Original entry on oeis.org

0, 1, 4, 9, 36, 64, 81, 100, 121, 144, 169, 196, 225, 324, 361, 400, 441, 484, 529, 576, 729, 900, 961, 1089, 1225, 1296, 1521, 1681, 1764, 1849, 2025, 2116, 2304, 2601, 2916, 3025, 3249, 3364, 3481, 3600, 3969, 4356, 4489, 4624, 4761, 5041, 5184, 5476, 5625

Offset: 1

Vincenzo Librandi, Jan 15 2016

Complement of A065408.

Includes A016766. - Robert Israel, Jan 15 2016

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000290, A016766, A065408, A104211.

[n^2: n in [0..80] | not IsPrime(&+Intseq(n^2))];

remove(t->isprime(convert(convert(t,base,10),`+`)), [seq(i^2,i=0..100)]); # Robert Israel, Jan 15 2016

Select[Range[0,100]^2, ! PrimeQ[Total[IntegerDigits[#]]] &]

is(n) = issquare(n) && !ispseudoprime(sumdigits(n)); \\ Altug Alkan, Jan 15 2016

a(1)=0 prepended by Altug Alkan Jan 15 2016

Edited by Bruno Berselli, Jan 15 2016

cp's OEIS Frontend

A028834 Numbers whose sum of digits is a prime.

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A104213 Primes with nonprime sums of digits.

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A219110 Numbers for which at least one sum of two adjacent digits is not prime.

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Mathematica

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A228019 Composite numbers whose sum of digits is a composite number.

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Magma

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PARI

A154679 Primes p such that the sum of digits of p+2 is a composite number.

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Maple

Mathematica

Extensions

A228020 Composite numbers whose initial, all intermediate and final iterated digit sums are composite numbers.

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Keywords

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Examples

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Crossrefs

Programs

Maple

Mathematica

PARI

A267430 Squares whose digit sum is not a prime.

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