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Search: id:A130704
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| A130704 |
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Palindromic primes whose squares are the sum of three consecutive primes. |
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+0
1
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| 7, 11, 151, 191, 929, 10301, 14741, 15451, 76667, 98689, 1062601, 1153511, 1175711, 1215121, 1300031, 1317131, 1489841, 1597951, 3075703, 3127213, 3362633, 3441443, 7354537, 7472747, 7662667, 9127219, 9196919, 9451549, 9561659
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The number of such palindromic primes less than 10^n: 1, 2, 5, 5, 10, 10, 30, 30, 141, 141, 843, 843, 5856, 5856, 42675, 42675, ....
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LINKS
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Robert G. Wilson v, Table of n, for n = 1..1000.
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FORMULA
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Intersection of A002385 and A034961.
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EXAMPLE
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7^2 = 49 = 13 + 17 + 19.
11^2 = 121 = 37 + 41 + 43.
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MATHEMATICA
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NextPalindrome[n_] := Block[{l = Floor[Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]]]] > FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[ idn, Ceiling[l/2]], Reverse[Take[idn, Floor[l/2]]]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[ idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]]]]]]]];
PrevPrim[n_] := Block[{k = n - 1}, While[ ! PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; fQ[n_] := Block[{p, q, r, s}, q = PrevPrim[ Ceiling[n^2/3]]; p = PrevPrim@q; r = NextPrim[ Floor[n^2/3]]; s = NextPrim@r; n^2 == p + q + r || n^2 == q + r + s];
pd = 6; lst = {}; Do[pd = NextPalindrome@pd; If[ PrimeQ@pd && fQ@pd, AppendTo[lst, pd]], {n, 10^8}]; lst
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CROSSREFS
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Sequence in context: A107187 A132958 A057737 this_sequence A038543 A145953 A154303
Adjacent sequences: A130701 A130702 A130703 this_sequence A130705 A130706 A130707
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KEYWORD
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base,nonn,less
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 19 2007
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