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A007921 Numbers that are not the difference of two primes. 19
7, 13, 19, 23, 25, 31, 33, 37, 43, 47, 49, 53, 55, 61, 63, 67, 73, 75, 79, 83, 85, 89, 91, 93, 97, 103, 109, 113, 115, 117, 119, 121, 123, 127, 131, 133, 139, 141, 143, 145, 151, 153, 157, 159, 163, 167, 169, 173, 175, 181, 183, 185, 187, 193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecturally, odd numbers n such that n+2 is composite.

Is this the same as A068780(2n-1) - 1? - J. Stauduhar, Aug 23 2012

A092953(a(n)) = 0. - Reinhard Zumkeller, Nov 10 2012

It seems that the sequence contains the squares of all primes except 2 and 3. - Ivan N. Ianakiev, Aug 29 2013

REFERENCES

F. Smarandache, Properties of Numbers, 1972. (See Smarandache odd sieve.)

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I.

F. Smarandache, Only Problems, Not Solutions!, 4th ed., 1993, Problem 94.

Index entries for primes, gaps between

PROG

(PARI) is(n)=n%2 && !isprime(n+2) \\ On Polignac's conjecture; Charles R Greathouse IV, Jun 28 2013

(Haskell)

a007921 n = a007921_list !! (n-1)

a007921_list = filter ((== 0) . a010051' . (+ 2)) [1, 3 ..]

-- Reinhard Zumkeller, Jul 03 2015

(Python)

from sympy import isprime

print [n for n in range(1, 200) if n%2 and not isprime(n + 2)] # Indranil Ghosh, Jun 15 2017, after Charles R Greathouse IV

CROSSREFS

Cf. A048859.

Complement of A030173. Cf. A001223.

Cf. also A005408, A010051.

Sequence in context: A274437 A031194 A121058 * A092409 A124095 A109369

Adjacent sequences:  A007918 A007919 A007920 * A007922 A007923 A007924

KEYWORD

nonn,easy,nice

AUTHOR

R. Muller

STATUS

approved

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Last modified August 9 12:53 EDT 2020. Contains 336323 sequences. (Running on oeis4.)