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.
NextPrime[ n_Integer ] := Module[ {k}, k = n + 1; While[ ! PrimeQ[ k ], k++ ]; k ]; c = d = p = q = 0; Do[ While[ d++; d <= 10^n, q = NextPrime[ q ]; p = p + Apply[ Plus, RealDigits[ q ] [[ 1 ] ]]; If[ PrimeQ[ p ], c++ ]]; d--; Print[ c ], {n, 0, 10} ]
n = 1000: prime set = {2, 5}, a[1000] = 7;
n = 255255: prime set={3, 5, 7, 11, 13, 17}, a[255255]= 3+5+7+2+4+8 = 29.
ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] Table[sdp[w], {w, 1, 150}]
Table[Total[Flatten[IntegerDigits[First/@FactorInteger[n]]]],{n,1,100}] (Zak Seidov)
from sympy import factorint def a(n): return sum(sum(map(int, str(p))) for p in factorint(n)) print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Dec 12 2023
a071317 n = a071317_list !! n a071317_list = scanl1 (+) a004159_list -- Reinhard Zumkeller, Apr 12 2014
s=0; Do[s=s+Apply[Plus, IntegerDigits[n^2]]; Print[s], {n, 1, 128}]
nxt[{n_,a_}]:={n+1,a+Total[IntegerDigits[(n+1)^2]]}; NestList[nxt,{0,0},60][[All,2]] (* Harvey P. Dale, Mar 09 2017 *)
FoldList[#1 + Total@ IntegerDigits[#2^2] &, 0, Range@ 55] (* Michael De Vlieger, Mar 25 2017 *)
Accumulate[Plus @@@ IntegerDigits[Range[0, 50]^2]] (* Giovanni Resta, Mar 25 2017 *)
from itertools import count, islice, accumulate def A071317_gen(): # generator of terms return accumulate(map(lambda n:sum(map(int,str(n**2))),count(0))) A071317_list = list(islice(A071317_gen(),20)) # Chai Wah Wu, Mar 15 2023
a(1) = 11//2//5//7//3 = 112573 = prime(10668). a(5) = 2//3//5//11//7 = 235117 = prime(20845). a(20) = 7//5//11//2//3 = 751123 = prime(60315).
catL := proc(L) local a,i,dgs ; a := op(1,L) ; for i from 2 to nops(L) do dgs := max(1, 1+ilog10(op(i,L))) ; a := a*10^dgs+op(i,L) ; end do: a ; end proc: A177275 := proc() local pL,a,c ; pL := [seq(ithprime(c),c=1..5)] ; a := {} ; for c in combinat[permute](pL) do p := catL(c) ; if isprime(p) then a := a union {p} ; end if; end do: print(sort(a)) ; end proc: A177275() ; # R. J. Mathar, May 09 2010
n=1000: A007953[1000]=1, prime set={2,5}, A095402[1000]=7, a[1000]=1-7=-6
ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] a=Table[sd[w], {w, 1, 150}];b=Table[sdp[w], {w, 1, 150}];b-a
n=85: digit sum=13, prime factor-digit sum=5+1+7=13, so 85 is here.
ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] a=Table[sd[w], {w, 1, 256}];b=Table[sdp[w], {w, 1, 150}];b-a; Flatten[Position[Sign[b-a], 0]]
Select[Range[2,300],Total[Flatten[IntegerDigits/@FactorInteger[#][[All, 1]]]] == Total[IntegerDigits[#]]&] (* Harvey P. Dale, Sep 29 2019 *)
a(4)=19 because A058049(4)= 5 and sum of digits of the first 5 primes, 2+3+5+7+(1+1)=19 is prime.
from sympy import isprime, nextprime
def sd(n): return sum(map(int, str(n)))
def aupto(limit):
alst, k, p, s = [], 1, 2, 2
while s <= limit:
if isprime(s): alst.append(s)
k += 1; p = nextprime(p); s += sd(p)
return alst
print(aupto(2579)) # Michael S. Branicky, Jul 18 2021
5 is a term because sum of digits of first 5 primes, 2+3+5+7+(1+1)=19, is prime. a(5) = 6 because in A051351(6) = 2 + 3 + 5 + 7 + 2 (sum of eleven's digits) + 4 (sum of thirteen's digits) which equals the sum of the digits through the sixth prime = 23 which itself is a prime.
s = 0; Do[ s = s + Apply[ Plus, RealDigits[ Prime[ n ]] [[1]] ]; If[ PrimeQ[ s ], Print[ n ] ], {n, 1, 1000} ]
isok(n) = isprime(sum(k=1, n, sumdigits(prime(k)))); \\ Michel Marcus, Mar 11 2017
from sympy import isprime, nextprime
def sd(n): return sum(map(int, str(n)))
def aupto(limit):
alst, k, p, s = [], 1, 2, 2
while k <= limit:
if isprime(s): alst.append(k)
k += 1; p = nextprime(p); s += sd(p)
return alst
print(aupto(306)) # Michael S. Branicky, Jul 18 2021
s=0; Do[s=s+Apply[Plus, IntegerDigits[n^3]]; Print[s], {n, 1, 128}]
nxt[{n_,a_}]:={n+1,a+Total[IntegerDigits[(n+1)^3]]}; NestList[nxt,{1,1},60][[;;,2]] (* Harvey P. Dale, Aug 30 2025 *)
n=24: digit sum=6, prime factor-digit sum=2+3=5, so 24 is here; n=153: digit sum=9, prime factor-digit sum=3+5+3=11>9, so 153 is here.
ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] a=Table[sd[w], {w, 1, 256}];b=Table[sdp[w], {w, 1, 150}];b-a; Flatten[Position[Sign[b-a], 1]]
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