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A115884
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Numbers k such that the k-th prime plus k gives a palindrome.
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6
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1, 2, 3, 4, 22, 45, 66, 71, 75, 88, 94, 97, 103, 105, 116, 140, 331, 432, 454, 565, 646, 703, 795, 1042, 1108, 1168, 1248, 1334, 1644, 1652, 1864, 1874, 1900, 2181, 2295, 2323, 2485, 2509, 2585, 2679, 2835, 2899, 2923, 3052, 3360, 3372, 3396, 3404
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OFFSET
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1,2
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LINKS
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EXAMPLE
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prime(103) + 103 = 666, a palindrome; so 103 is term.
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MAPLE
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filter:= proc(n) local p, L;
p:= ithprime(n)+n;
L:= convert(p, base, 10);
ListTools:-Reverse(L) = L
end proc:
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MATHEMATICA
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palQ[n_]:=Module[{idn=IntegerDigits[n]}, idn==Reverse[idn]]; With[ {nn=3500}, Rest[Flatten[Position[Total/@Thread[{Prime[Range[nn]], Range[nn]}], _?(palQ)]]]] (* Harvey P. Dale, Oct 11 2011 *)
palQ[n_] := Reverse[x = IntegerDigits[n]] == x; Select[Range[3405], palQ[Prime[#] + #] &] (* Jayanta Basu, Jun 24 2013 *)
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PROG
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(PARI) ispal(n) = my(e=digits(n)); e == Vecrev(e) \\ A002113
for(k=1, 10^6, b=k+prime(k); if(ispal(b), print1(k, ", "))) \\ Alexandru Petrescu, Jun 15 2022
(Python)
from sympy import nextprime
def ispal(n): s = str(n); return s == s[::-1]
def agen(): # generator of terms
k, pk = 1, 2
while True:
if ispal(k+pk): yield k
k, pk = k+1, nextprime(pk)
g = agen()
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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