This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
69999899 is a prime with sum of the digits = 68, hence belongs to the sequence.
[p: p in PrimesUpTo(100000000) | &+Intseq(p) eq 68];
Select[Prime[Range[10000000]], Total[IntegerDigits[#]]==68 &]
# see code in A107579: the same code can be used to produce this sequence, by giving the initial term p = 6*10**7-1, for digit sum 68. - M. F. Hasler, Mar 16 2022
3001 is a prime with sum of digits = 4, hence belongs to the sequence.
[p: p in PrimesUpTo(800000000) | &+Intseq(p) eq 4]; // Vincenzo Librandi, Jul 08 2014
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
Union[FromDigits/@Select[Flatten[Table[Tuples[{0,1,2,3},k],{k,9}],1],PrimeQ[FromDigits[#]]&&Total[#]==4&]] (* Jayanta Basu, May 19 2013 *)
FromDigits/@Select[Tuples[{0,1,2,3},10],Total[#]==4&&PrimeQ[FromDigits[#]]&] (* Harvey P. Dale, Jul 23 2025 *)
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
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. M. F. Hasler, Mar 09 2022
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) \\ M. F. Hasler, Mar 09 2022
1301 belongs to the sequence since it is a prime with sum of digits = 5.
[p: p in PrimesUpTo(250000) | &+Intseq(p) eq 5]; // Vincenzo Librandi, Jul 08 2014
T:= n-> `if`(n=1, 5, sort(select(isprime, [seq(seq(seq(
10^(n-1)+1+10^i+10^j+10^k, k=1..j), j=1..i), i=1..n-1),
seq(10^(n-1)+3+10^i, i=1..n-1)]))[]):
seq(T(n), n=1..8); # Alois P. Heinz, Dec 28 2015
Select[Prime[Range[20000]],Total[IntegerDigits[#]]==5&] (* Harvey P. Dale, Nov 24 2013 *)
\\ From M. F. Hasler, Mar 09 2022: (Start) select( {is_A062341(p,s=5)=sumdigits(p)==s&&isprime(p)}, primes([1,10^6])) \\ 2nd optional parameter for similar sequences with other digit sums. A062341_upto_length(L,s=5,a=List(),u=[10^k|k<-[0..L-1]])={forvec(d=[[1,L]|i<-[1..s]], isprime(p=vecsum(vecextract(u,d))) && listput(a,p),1); Set(a)} \\ (End)
from sympy import primerange as primes def ok(p): return sum(map(int, str(p))) == 5 print(list(filter(ok, primes(1, 202002)))) # Michael S. Branicky, May 23 2021
1151 belongs to the sequence since it is a prime with sum of digits = 8.
[p: p in PrimesUpTo(20000) | &+Intseq(p) eq 8]; // Vincenzo Librandi, Jul 08 2014
A062343 := proc(n) option remember ; local p ; if n = 1 then 17; else p := nextprime(procname(n-1)) ; while true do if digsum(p) = 8 then # digsum in oeis.org/transforms.txt return p; else p := nextprime(p) ; end if; end do: end if; end proc: seq(A062343(n),n=1..80) ; # R. J. Mathar, May 22 2025
Select[Prime[Range[500000]], Total[IntegerDigits[#]]==8 &] (* Vincenzo Librandi, Jul 08 2014 *)
select( {is_A062343(p, s=8)=sumdigits(p)==s&&isprime(p)}, primes([1, 12345])) \\ 2nd optional parameter for similar sequences with other digit sums. M. F. Hasler, Mar 09 2022
{A062343_upto_length(L, s=8, 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)} \\ M. F. Hasler, Mar 09 2022
349 is a prime with sum of digits =16=4*4, hence belongs to the sequence.
[ p: p in PrimesUpTo(10000) | &+Intseq(p) mod 4 eq 0 ]; /* Vincenzo Librandi, Apr 02 2011 */
filter:= x -> (convert(convert(x,base,10),`+`) mod 4 = 0) and isprime(x); A062338:= select(filter, [seq(2*i+1,i=0..1000)]); # Robert Israel, Apr 20 2014
is(n)=isprime(n) && sumdigits(n)%4==0 \\ Charles R Greathouse IV, Mar 09 2022
Select[Prime[Range[11000]],DigitCount[#,10,0]==0&&Total[ IntegerDigits[ #]] == 7&] (* Harvey P. Dale, Dec 04 2020 *)
isok(n) = isprime(n) && (sumdigits(n) == 7) && (vecmin(digits(n)) != 0); \\ Michel Marcus, Oct 10 2013
23(1=3-2), 43(1=abs(3-4)), 67(1=abs(7-6)), 89(1=abs(9-8)), 113(1=3-(1+1)).
ps1[n_]:=Module[{idn=IntegerDigits[n]},Abs[Last[idn]-Total[Most[idn]]] == 1]; Select[Prime[Range[400]],ps1] (* Harvey P. Dale, Jul 31 2012 *)
a(n)=n--; my(A,B,C,D); sum(a=0,n, A=10^n+10^a+1; sum(b=a,n, B=A+10^b; sum(c=b,n, C=B+10^c; sum(d=c,n, D=C+10^d; sum(e=d,n, isprime(D+10^e)))))) \\ Charles R Greathouse IV, Jun 19 2015
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