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
[a: n in [0..250] | IsPrime(a) where a is 9*n - 1 ]; // Vincenzo Librandi, Jun 07 2015
select(isprime, [seq(18*i-1,i=1..1000)]); # Robert Israel, Sep 03 2014
Select[ Range[ 2500 ], PrimeQ[ # ] && Mod[ #, 9 ] == 8 & ] Select[9*Range[300] - 1, PrimeQ]
select( {is(n)=n%9==8&&isprime(n)}, primes([1,2000])) \\ M. F. Hasler, Mar 10 2022
from sympy import prime A061242 = [p for p in (prime(n) for n in range(1,10**3)) if not (p+1) % 18] # Chai Wah Wu, Sep 02 2014
[p: p in PrimesUpTo(10000) | &+Intseq(p) eq 10]; // Vincenzo Librandi, Jul 08 2014
a:=proc(n) local nn: nn:=convert(n,base,10): if isprime(n)=true and add(nn[j], j=1..nops(nn))=10 then n else end if end proc: seq(a(n),n=1..10^4); # Emeric Deutsch, Mar 06 2008
Select[Prime[Range[100000]], Total[IntegerDigits[#]]==10 &] (* Vincenzo Librandi, Jul 08 2014 *)
forprime(p=19,8101,if(10==sumdigits(p),print(p","))) \\ Zak Seidov, Oct 08 2016
(A107579_nxt(p)=until(isprime(p=A228915(p)),); p); A107579_first(N=100)=vector(N, i, p=if(i>1, A107579_nxt(p), 19)) \\ M. F. Hasler, Mar 15 2022
from itertools import count, islice
from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def agen(b=10, sod=10): # generator for any base, sum-of-digits
if 0 <= sod < b:
yield sod
nzdigs = [i for i in range(1, b) if i <= sod]
nzmultiset = []
for d in range(1, b):
nzmultiset += [d]*(sod//d)
for d in count(2):
fullmultiset = [0]*(d-1-(sod-1)//(b-1)) + nzmultiset
for firstdig in nzdigs:
target_sum, restmultiset = sod - int(firstdig), fullmultiset[:]
restmultiset.remove(firstdig)
for p in multiset_permutations(restmultiset, d-1):
if sum(p) == target_sum:
t = int("".join(map(str, [firstdig]+p)), b)
if isprime(t):
yield t
if p[0] == target_sum:
break
print(list(islice(agen(), 45))) # Michael S. Branicky, Mar 10 2022
from sympy import isprime def A107579(p=19): "Return a generator of the sequence of all primes >= p with the same digit sum as p." while True: if isprime(p): yield p p = A228915(p) # skip to next larger integer with the same digit sum a=A107579(); [next(a) for in range(50)] # _M. F. Hasler, Mar 16 2022
[p: p in PrimesUpTo(69000000) | &+Intseq(p) eq 64]; // Vincenzo Librandi, Jul 09 2014
Select[Prime[Range[3600000]],Total[IntegerDigits[#]]==64&] (* Harvey P. Dale, Jan 19 2012 *)
[p: p in PrimesUpTo(38000000) | &+Intseq(p) eq 62]; // Vincenzo Librandi, Jul 09 2014
Select[Prime[Range[600000]], Total[IntegerDigits[#]]==62 &] (* Vincenzo Librandi, Jul 09 2014 *)
[p: p in PrimesUpTo(69000000) | &+Intseq(p) eq 65]; // Vincenzo Librandi, Jul 09 2014
Select[Prime[Range[600000]], Total[IntegerDigits[#]]==65 &] (* Vincenzo Librandi, Jul 09 2014 *)
[p: p in PrimesUpTo(90000000) | &+Intseq(p) eq 67]; // Vincenzo Librandi, Jul 09 2014
F:= proc(t,d)
if d = 1 then
if t<=9 then return [t] else return [] fi
fi;
if t > 9*d then return [] fi;
[seq(op(map(x -> a*10^(d-1)+x, procname(t-a,d-1))), a=0..min(9,t))]
end proc:
select(isprime, F(67,8)); # Robert Israel, Mar 25 2018
Select[Prime[Range[600000]], Total[IntegerDigits[#]]==67 &] (* Vincenzo Librandi, Jul 09 2014 *)
isok(n) = isprime(n) && (sumdigits(n) == 67); \\ Altug Alkan, Mar 25 2018
709 is a prime with sum of digits = 16, hence belongs to the sequence.
[ p: p in PrimesUpTo(10000) | &+Intseq(p) mod 8 eq 0 ]; // Vincenzo Librandi, Apr 02 2011
Select[Prime[Range[500]],Divisible[Total[IntegerDigits[#]],8]&] (* Harvey P. Dale, Jun 23 2011 *)
is(n)= sumdigits(n)%8==0 && isprime(n) \\ Charles R Greathouse IV, Mar 09 2022
Comments