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A089056
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Primes whose sum of digits [s(d)] is a prime and where sum of two such consecutive s(d) values is a square.
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1
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7, 11, 23, 29, 41, 131, 137, 197, 199, 467, 487, 557, 577, 593, 757, 773, 827, 829, 863, 881, 883, 937, 953, 1013, 1019, 1031, 1103, 1109, 1277, 1279, 1567, 1583, 1637, 1657, 1871, 1873, 2003, 2027, 2087, 2089, 2267, 2269, 2377, 2393, 2447, 2467, 2591, 2593
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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From the sequence of primes whose s(d) values are prime, select those where sum of two consecutive s(d) values is a square.
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EXAMPLE
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a(2)=23; a(3)=29: 2+3=5; 2+9=11; 5+11=16, a square.
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MATHEMATICA
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Module[{sdp=Select[Prime[Range[500]], PrimeQ[Total[IntegerDigits[#]]]&]}, Flatten[Select[ Partition[ sdp, 2, 1], IntegerQ[ Sqrt[ Total[ Flatten[ IntegerDigits/@ #]]]]&]]]//Union (* Harvey P. Dale, Oct 09 2023 *)
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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