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A089824
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Primes p such that the next prime after p can be obtained from p by adding the sum of the digits of p.
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3
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11, 13, 101, 103, 181, 293, 631, 701, 811, 1153, 1171, 1409, 1801, 1933, 2017, 2039, 2053, 2143, 2213, 2521, 2633, 3041, 3089, 3221, 3373, 3391, 3469, 3643, 3739, 4057, 4231, 5153, 5281, 5333, 5449, 5623, 5717, 6053, 6121, 6301, 7043, 7333, 8101, 8543, 9241
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OFFSET
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1,1
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COMMENTS
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I call these primes (additive) "pointer primes", in the sense that such primes p "point" to the next prime after p when the sum of the digits of p is added to p.
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LINKS
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EXAMPLE
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13 + sum of digits of 13 = 17, which is the next prime after 13. Hence 13 belongs to the sequence.
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MAPLE
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a:= proc(n) option remember; local p, q;
p:= a(n-1); q:= nextprime(p);
do p:= q; q:= nextprime(p);
if add(i, i=convert(p, base, 10))=q-p then break fi
od; p
end: a(1):= 11:
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MATHEMATICA
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r = {}; Do[p = Prime[i]; q = Prime[i + 1]; If[p + Apply[Plus, IntegerDigits[p]] == q, r = Append[r, p]], {i, 1, 10^6}]; r
Transpose[Select[Partition[Prime[Range[1000]], 2, 1], #[[2]]==#[[1]]+Total[ IntegerDigits[ #[[1]]]]&]][[1]] (* Harvey P. Dale, Apr 20 2013 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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