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A084747
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Leading diagonal of triangle shown below in which the n-th row contains the n smallest numbers > 0 such that when they are incremented by n yield a prime.
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2
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1, 3, 8, 9, 14, 17, 24, 29, 32, 33, 42, 47, 54, 57, 58, 63, 72, 79, 84, 87, 88, 91, 108, 113, 114, 123, 124, 129, 138, 143, 150, 159, 160, 163, 164, 175, 190, 191, 194, 199, 210, 215, 226, 227, 232, 235, 246, 259, 262, 263, 266, 279, 294, 295, 298, 303, 310, 315
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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1;
1, 3;
2, 4, 8;
1, 3, 7, 9;
2, 6, 8, 12, 14;
1, 5, 7, 11, 13, 17;
4, 6, 10, 12, 16, 22, 24;
...
so sequence is 1, 3, 8, 9, 14, 17, 24, ... = A084695(n, n).
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MATHEMATICA
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Table[Prime[PrimePi[n] +n] -n, {n, 80}] (* G. C. Greubel, May 12 2023 *)
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PROG
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(PARI) a(n) = prime(primepi(n) + n) - n; \\ Michel Marcus, Mar 28 2021
(Magma) [NthPrime(#PrimesUpTo(n) +n) -n: n in [1..80]]; // G. C. Greubel, May 12 2023
(SageMath)
def A084747(n): return nth_prime(prime_pi(n) + n) - n
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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