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Search: id:A058049
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| A058049 |
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Numbers n such that the sum of the digits through the n-th prime is itself a prime. |
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+0
2
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| 1, 2, 4, 5, 6, 7, 8, 11, 12, 14, 23, 33, 43, 45, 48, 64, 69, 72, 73, 77, 87, 94, 95, 96, 98, 110, 118, 124, 130, 133, 140, 148, 152, 154, 157, 162, 171, 174, 178, 181, 196, 200, 201, 206, 210, 212, 219, 232, 241, 244, 253, 257, 267, 269, 272, 277, 299, 304, 306
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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What is intriguing about this sequence is that the number of primes less than 10^m is of the same magnitude as A006880. Here they begin 7, 25, 122, 934.
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LINKS
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Z. Stankova-Frenkel and J. West, Explicit enumeration of 321,hexagon-avoiding permutations.
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EXAMPLE
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a(5) = 6 because in A051351(6) = 2 + 3 + 5 + 7 + 2 (sum of eleven's digits) + 4 (sum of thirteen's digits) which equals the sum of the digits through the sixth prime = 23 which itself is a prime.
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MATHEMATICA
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s = 0; Do[ s = s + Apply[ Plus, RealDigits[ Prime[ n ]] [[1]] ]; If[ PrimeQ[ s ], Print[ n ] ], {n, 0, 1000} ].
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CROSSREFS
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Cf. A007605 and A051351.
Sequence in context: A101742 A111688 A104248 this_sequence A091871 A039085 A026486
Adjacent sequences: A058046 A058047 A058048 this_sequence A058050 A058051 A058052
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 18 2000
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