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Search: id:A070247
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| A070247 |
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Palindromic primes with digit sum 5. |
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+0
5
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| 5, 131, 10301, 1003001, 100030001, 100111001, 101000010000101, 10000010101000001, 101000000010000000101, 110000000010000000011, 10000000000300000000001, 10000100000100000100001
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It is conjectured that are just 3 palindromic primes with digit sum 2, namely 2, 11 and 101. If any others exist, they must be of the form 10^(2^k) +1 with k > 14.
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REFERENCES
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H. Riesel, "Some factors of the numbers Gn = 6^2^n + 1 and Hn = 10^2^n + 1," Math. Comp., 23:106 (1969) 413-415.
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MATHEMATICA
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Do[p = Join[ IntegerDigits[n, 4], Reverse[ Drop[ IntegerDigits[n, 4], -1]]]; q = Plus @@ p; If[q == 5 && PrimeQ[ FromDigits[p]] && q == 5, Print[ FromDigits[p]]], {n, 1, 4 10^8}] (* this coding will not pick up the first entry *)
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CROSSREFS
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Cf. A002385, A070248 & A070249.
Adjacent sequences: A070244 A070245 A070246 this_sequence A070248 A070249 A070250
Sequence in context: A003732 A048434 A142892 this_sequence A003372 A135758 A053517
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 05 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), May 15 2002
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