A066277 - OEIS

A066277

Primes p(m) such that a prime number q exists so that p(m)-q = c(m), the m-th composite number.

2, 3, 5, 7, 17, 23, 29, 31, 41, 43, 67, 89, 97, 131, 139, 157, 281, 311, 313, 331, 353, 379, 401, 431, 449, 499, 569, 571, 607, 631, 683, 733, 743, 751, 787, 829, 881, 883, 947, 967, 983, 1033, 1091, 1117, 1123, 1151, 1301, 1303, 1327, 1373, 1543, 1559

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OFFSET

1,1

COMMENTS

Number of terms < 10^k: 4, 13, 41, 177, 1119, 6963, 48647, 359109, 2766164, ..., . - Robert G. Wilson v, Dec 11 2017

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = prime(A060253(n)) or A000040(A060253(n)). - Michel Marcus, Dec 11 2017

EXAMPLE

p(25) = A000040(25) = 97; 97 - 61 = A002808(25) = c(25) = 38 and 61 is prime.

MATHEMATICA

Composite[n_Integer] := FixedPoint[n + PrimePi@# +1 &, n + PrimePi@n +1]; fQ[n_] := PrimeQ[Prime@n - Composite@n]; Prime@ Select[ Range@250, fQ] (* Robert G. Wilson v, Dec 11 2017 *)

CROSSREFS

Cf. A000040, A002808, A038529, A060253.

Sequence in context: A319823 A286499 A116947 * A360383 A164134 A152184

Adjacent sequences: A066274 A066275 A066276 * A066278 A066279 A066280

KEYWORD

nonn

AUTHOR

Labos Elemer, Dec 10 2001

STATUS

approved