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.
a(3)=694 because the 3rd perfect number is 496.
109 is in the list because it is the sum of R(47)+R(53)=74+35=109.
Take[Union[Total[IntegerReverse[#]]&/@Partition[Prime[Range[500]],2,1]],100] (* The program is not suitable for more than 100 or so terms. *) (* Harvey P. Dale, Apr 26 2022 *)
582 = R(191) + R(193) = 191 + 391 and R(683) + R(691) = 386 + 196. 1032 = R(113) + R(127) = 311 + 721 = R(613) + R(617) = 316 + 716.
read("transforms") ; A055642 := proc(n) max(1, ilog10(n)+1) ; end:
A004087 := proc(n) option remember; digrev(ithprime(n)) ; end:
isA162705 := proc(n) c := 0 ; for i from 1 do p := ithprime(i) ; if A055642(p) > A055642(n) then break; fi; if A004087(i)+A004087(i+1) = n then c := c+1; fi; od: RETURN(c > 1); end:
for n from 1 to 10000 do if isA162705(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Jul 13 2009
Sort[Transpose[Select[Tally[FromDigits[Reverse[IntegerDigits[#[[1]]]]] + FromDigits[Reverse[IntegerDigits[#[[2]]]]]&/@Partition[Prime[Range[ 2000]],2,1]],Last[#]>1&]][[1]]] (* Harvey P. Dale, Nov 14 2012 *)
(from primes 11, 13, and 17): 11 + 31 + 71 = 113; (from primes 13, 17, and 19): 31 + 71 + 91 = 193; (from primes 173, 179, and 181): 371 + 971 + 181 = 1523.
r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Table[r[Prime[n]] + r[Prime[n+1]] + r[Prime[n+2]], {n, 50}]
a(12) = min {k such that k|R(12) and k = p*q for primes p and q (not necessarily distinct)} = min {k, k|21 and k semiprime} = 21 = 3*7.
a(42) = min {k, k|24 and k semiprime} = min {4,6} = 4 = 2*2.
r:= proc(n) option remember; local q;
`if`(n<10, n, irem(n, 10, 'q') *10^(length(n)-1)+r(q))
end:
a:= proc(n) local m, k;
m:= r(n);
for k from 4 to m do
if irem(m, k)=0 and not isprime(k) and
add(i[2], i=ifactors(k)[2])=2 then return k fi
od; 0
end:
seq(a(n), n=1..100); # Alois P. Heinz, Mar 26 2012
spd[n_]:=Module[{sps=Select[Divisors[FromDigits[Reverse[ IntegerDigits[n]]]], PrimeOmega[#] == 2&,1]},If[sps=={},0,First[sps]]]; Array[spd,80] (* Harvey P. Dale, Aug 12 2012 *)
a(2)= 13, it is prime: n= 6, prime(6)= 13: reversal(13^2+13)= 281, which is also prime. a(4)= 103, it is prime: n= 27, prime(27)= 103: reversal(103^2+103)= 21701, which is also prime. a(6)= 181, it is prime: n= 42, prime(42)= 181: reversal(181^2+181)= 24923, which is also prime.
with(StringTools): KD:= proc() local a, p; p:=ithprime(n); a:= parse(Reverse(convert((p^2+p), string))); if isprime(a) then RETURN (p): fi; end: seq(KD(), n=1..3000);
Select[Prime[Range[3000]], PrimeQ[FromDigits[Reverse[IntegerDigits[#^2 + #]]]] &]
9 is in the list because 9 = 3*3 is a semiprime and reverse(3) = 3 is prime. 143 is in the list because 143 = 11*13 is a semiprime and both reverse(11) = 11 and reverse(13) = 31 are prime.
With[{nn=250},Take[Union[Times@@@Select[Tuples[IntegerReverse/@Prime[Range[nn]],2],AllTrue[#,PrimeQ]&]],60]] (* Harvey P. Dale, Apr 27 2025 *)
reverse = lambda n: sum([10^i*int(str(n)[i]) for i in range(len(str(n)))])
def is_semirp(n):
F = factor(n)
if sum([f[1] for f in F])==2:
r, p = F[0][0], F[-1][0]
if is_prime(reverse(r)) and is_prime(reverse(p)): return True
[a for a in range(1,356) if is_semirp(a)] # Danny Rorabaugh, Nov 25 2015
For n = 8, 2^n - 1 = 255, so 552 is in the sequence. - _Michael B. Porter_, Jul 02 2016
[Seqint(Reverse(Intseq(2^n-1))): n in [0..40]];
Table[FromDigits[Reverse[IntegerDigits[2^n-1]]], {n, 0, 75}]
a(n) = eval(concat(Vecrev(Str(2^n-1)))) \\ Felix Fröhlich, Jul 03 2016
a(4) = 358 is a term because 358 = A071602(11) is the sum of the reverses of the first 11 primes, and is the reverse of the prime 853. A071602(7) = 130 is not a term, because 130 is not the reverse of a prime, even though the reverse of 130 is a prime.
rev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc: PR:= map(rev, select(isprime, [$1..10000]): SPR:= ListTools:-PartialSums(PR): select(t -> t mod 10 <> 0 and isprime(rev(t)),SPR);
# Check if number is Chen prime ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then return 'true' else return 'false' fi fi end: #Reverse digits obrni_stev:=proc(n) local i, tren, tren1, st, ans; ans:=[ ]: tren:=n: tren1:=0: for i while (tren>0) do st:=round(10*frac(tren/10)): ans:=[op(ans), st]: tren:=trunc(tren/10): od: for i from 0 to nops(ans)-1 do tren1:= tren1 + op(nops(ans)-i, ans)*10^(i): od: return tren1 end: ts_inv_chen_pra:= proc(n) local i, trens, ans; trens:= [ ]; ans:=[ ]; for i from 1 to n do if (ischenprime( i ) = 'true') then ans:=[op(ans),obrni_stev(i)] fi: od: return ans end: ts_inv_chen_pra(2000);
psp=Take[Union[Join[Union[Times@@@Tuples[Prime[Range[100]],{2}]],Prime[Range[PrimePi[250000]]]]],200];
FromDigits[Reverse[IntegerDigits[#]]]&/@(Select[Prime[Range[PrimePi[1000]]],MemberQ[psp,#+2]&]) (* Harvey P. Dale, Feb 08 2011 *)
Comments