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A339414
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Primes p such that (p+q)/4 is prime, where q is the next prime after p.
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2
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3, 5, 23, 31, 83, 131, 251, 271, 331, 383, 443, 563, 971, 1123, 1223, 1231, 1283, 1291, 1543, 2063, 2371, 2383, 2551, 2851, 2903, 2963, 3083, 3323, 3691, 3889, 4051, 4283, 4591, 4733, 4831, 4871, 4951, 5003, 5209, 5351, 5683, 5711, 5851, 6229, 6271, 6323, 6491, 6863, 6911, 7393, 7451, 7583, 7643
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OFFSET
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1,1
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COMMENTS
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After the initial 2 terms, a(n)=2*A118134(n)-3. - Hugo Pfoertner, Dec 03 2020
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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a(5)=83 is in the sequence because it is prime, the next prime is 89, and (83+89)/4 = 43 is prime.
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MAPLE
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P:= select(isprime, [seq(i, i=3..10000, 2)]):
R:= (P[1..-2]+P[2..-1])/4:
P[select(i-> R[i]::integer and isprime(R[i]), [$1..nops(R)])];
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PROG
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(PARI) isok(p) = isprime(p) && iferr(isprime((p+nextprime(p+1))/4), E, 0); \\ Michel Marcus, Dec 04 2020
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CROSSREFS
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Subset of A098058.
Cf. A118134.
Sequence in context: A106307 A106282 A163153 * A238199 A296927 A215132
Adjacent sequences: A339411 A339412 A339413 * A339415 A339416 A339417
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KEYWORD
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nonn
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AUTHOR
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Robert Israel, Dec 03 2020
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STATUS
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approved
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