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A064233 Numbers that are not the sum of a prime number and a nonzero square. 7
1, 2, 5, 10, 13, 25, 31, 34, 37, 58, 61, 64, 85, 91, 121, 127, 130, 169, 196, 214, 226, 289, 324, 370, 379, 400, 439, 526, 529, 571, 625, 676, 706, 730, 771, 784, 829, 841, 991, 1024, 1089, 1225, 1255, 1351, 1414, 1444, 1521, 1549, 1681, 1849, 1906, 1936, 2116 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is infinite, cf. A014090. Subsequence of squares = A053726^2. Subsequence of nonsquares is disjoint union of A020495 and A065377 and so is probably finite. - Vladeta Jovovic, Apr 02 2005

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

I. V. Poljakov, On the exceptional set for the sum of a prime and a perfect square, 1982 Math. USSR Izv. 19 611.

EXAMPLE

5 = 1+4 or 2+3; a prime and a square do not appear together in either sum.

MATHEMATICA

Complement[ Table[ n, {n, 1, 10000} ], Union[ Flatten[ Table[ Prime[ i ] + j^2, {i, 1, 1230}, {j, 1, 100} ] ] ] ]

PROG

(PARI) list(lim)=my(v=vectorsmall(lim\1, i, 1), u=List(), b); forprime(p=2, #v, b=0; while((t=p+b++^2)<=#v, v[t]=0)); for(i=1, #v, if(v[i], listput(u, i))); Vec(u) \\ Charles R Greathouse IV, May 29 2012

CROSSREFS

Sequence in context: A135467 A230550 A018571 * A051952 A103188 A281229

Adjacent sequences:  A064230 A064231 A064232 * A064234 A064235 A064236

KEYWORD

nonn,nice

AUTHOR

Axel Harvey, Sep 22 2001

EXTENSIONS

More terms from Vladeta Jovovic, Robert G. Wilson v and Felice Russo, Sep 23 2001

STATUS

approved

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Last modified November 15 07:53 EST 2018. Contains 317225 sequences. (Running on oeis4.)