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.
t = {s = 2}; Do[If[(y = Total[IntegerDigits[x = Prime[n]]]) >= s, AppendTo[t, x]; s = y], {n, 2, 2500}]; t (* Jayanta Basu, Aug 10 2013 *)
"SOD" = "sum of digits": a(5) = 113, the prime whose index is 30. SOD(30) = 3 and SOD(113) = 5. Since 3 < 5 and 5 is nextprime to 3, adjoin 113 to the sequence.
10 'use of str,mid,len,val 20 'in SOD prime index and SOD prime 30 Y=1 40 Y=nxtprm(Y) 50 C=C+1:print C;Y;"-"; 60 D=str(C):Z=str(Y) 70 E=len(D):F=len(Z) 80 for Q=2 to E 90 A=mid(D,Q,1):G=val(A) 100 I=I+G:print I; 110 next Q 120 for R=2 to F 130 B=mid(Z,R,1):H=val(B) 140 J=J+H:print J; 150 next R 160 if I=prmdiv(I) and J=prmdiv(J) and I>J and I=nxtprm(J) then stop 170 I=0:J=0 180 goto 40
If n = 16 then prime(n) = 53 and abs((5+3)-(1+6)) = 8-7 = 1, so 16 is in the sequence.
Select[Range[500], Abs[Apply[Plus, RealDigits[Prime[#]][[1]]] - Sum[DigitCount[#][[i]]*i, {i, 9}]] < 2 &] (* G. C. Greubel, Sep 10 2016 *)
list(lim)=my(v=List(),n); forprime(p=2,, if(n++>lim,break); if(abs(sumdigits(n)-sumdigits(p))<2, listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Sep 10 2016
For p=1571 (prime), 1+5+7 = 13; 13*10 = 130; 130+1 = 131 (prime).
map(t -> 10*convert(convert(t,base,10),`+`)-9*(t mod 10), [seq(ithprime(i),i=1..100)]); # Robert Israel, Mar 25 2018
Array[10 Total@ # - 9 Last@ # &@ IntegerDigits[Prime@ #] &, 67] (* Michael De Vlieger, Apr 27 2018 *)
a(n) = my(p=prime(n); d=p % 10); sumdigits(p-d)*10+d; \\ Michel Marcus, Mar 23 2018
Prime(5) = 11, 1 + 1 = 2 hence a(5) = 2. a(297)=7 because the 297th prime is 1951 and 1+9+5+1 = 16 -> 1+6 = 7.
a038194 = flip mod 9 . a000040 -- Reinhard Zumkeller, Dec 10 2014
[p mod 9: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014
A038194 := proc(n) return ithprime(n) mod 9: end: seq(A038194(n), n=1..100); # Nathaniel Johnston, May 04 2011
Table[Mod[Prime[n], 9], {n, 200}]
Mod[Prime[Range[100]], 9] (* Vincenzo Librandi, May 06 2014 *)
forprime(p=2,600,print1(p%9,","))
131 is the 32nd prime and sum of digits of both is 5.
a033548 n = a033548_list !! (n-1) a033548_list = filter ((== 0) . a090431 . a049084) a000040_list -- Reinhard Zumkeller, Mar 16 2014
read("transforms") :
isA033548 := proc(n)
if isprime(n) and digsum(n) = digsum(numtheory[pi](n)) then
true ;
else
false;
end if;
end proc:
A033548 := proc(n)
local p, k;
if n = 1 then
131;
else
p := nextprime(procname(n-1)) ;
while true do
if isA033548(p) then
return p;
end if;
p := nextprime(p) ;
end do:
end if;
end proc:
seq(A033548(n),n=1..40) ; # R. J. Mathar, Jul 07 2021
Prime[ Select[ Range[ 2000 ], Apply[ Plus, IntegerDigits[ # ] ] == Apply[ Plus, IntegerDigits[ Prime[ # ] ] ] & ] ] (* Santi Spadaro, Oct 14 2001 *) Select[ Prime@ Range@ 5927, Plus @@ IntegerDigits@ # == Plus @@ IntegerDigits@ PrimePi@ # &] (* Robert G. Wilson v, Jun 07 2009 *) nn=800;Transpose[Select[Thread[{Prime[Range[nn]],Range[nn]}],Total[IntegerDigits[First[#]]]== Total[ IntegerDigits[ Last[#]]]&]][[1]] (* Harvey P. Dale, Jun 13 2011 *)
is(n)=isprime(n) && sumdigits(n)==sumdigits(primepi(n)) \\ Charles R Greathouse IV, Jun 18 2015
from sympy.ntheory.factor_ import digits from sympy import primepi, primerange print([n for n in primerange(1, 5901) if (sum(digits(n)[1:])==sum(digits(primepi(n))[1:]))]) # Indranil Ghosh, Jun 27 2017, after Charles R Greathouse IV
Table[ Sum[ Apply[ Plus, RealDigits[ Prime[ j ]] [[1]] ], {j, 1, n} ], {n, 1, 100} ]
a(n) = vecsum(apply(sumdigits, primes(n))); \\ Michel Marcus, Aug 28 2023
131 is the 32nd prime and sum of digits of both is 5.
a033549 n = a033549_list !! (n-1) a033549_list = filter ((== 0) . a090431) [1..] -- Reinhard Zumkeller, Mar 16 2014
Select[Range[1000],Total[IntegerDigits[#]]==Total[IntegerDigits[ Prime[#]]]&] (* Harvey P. Dale, May 05 2011 *)
is(n,p=prime(n))=sumdigits(n)==sumdigits(p) \\ Charles R Greathouse IV, Feb 07 2017
from sympy.ntheory.factor_ import digits from sympy import prime print([n for n in range(1, 1001) if sum(digits(n)[1:])==sum(digits(prime(n))[1:])]) # Indranil Ghosh, Jun 27 2017
a(7)=89 because 8+9=17 and 17 is the 7th prime.
a[n_]:=Module[{k=2}, While[DigitSum[k]!=Prime[n], k=NextPrime[k]]; k]; Array[a,15] (* Stefano Spezia, Mar 27 2025 *)
a(n) = {my(k=2); my(p=prime(n)); while((sumdigits(k) != prime(n)), k=nextprime(k+1)); k;} \\ Michel Marcus, Nov 01 2015
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