A309152 - OEIS

A309152

Numbers that can be written as the sum of two primes whose difference is also prime.

7, 8, 9, 12, 15, 21, 24, 33, 36, 45, 60, 63, 75, 84, 105, 111, 120, 141, 144, 153, 183, 195, 201, 204, 216, 231, 243, 273, 276, 285, 300, 315, 351, 360, 384, 396, 423, 435, 456, 465, 480, 525, 540, 564, 573, 603, 621, 624, 645, 663, 696, 813, 825, 831, 840

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OFFSET

1,1

COMMENTS

Numbers k such that k = p + q where p < q and p, q, and q - p are all prime.

Union of A054735 and (A006512 + 2). - Robert Israel, Jul 15 2019

From Bernard Schott, Jul 15 2019: (Start)

If k is even, then k is in A054735 with q - p = 2.

If k is odd, then k is in (A006512 + 2) with p = 2. (End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

P:= select(isprime, {seq(i, i=3..10000, 2)}):

T:= P intersect map(`+`, P, 2):

A1:= map(`+`, T, 2):

A2:= select(`<`, map(t -> 2*t-2, T), max(A1)):

sort(convert(A1 union A2, list); # Robert Israel, Jul 15 2019

PROG

(PARI) is(n) = my(x=n-1, y=1); while(x >= y, if(ispseudoprime(x) && ispseudoprime(y), if(ispseudoprime(x-y), return(1))); x--; y++); 0 \\ Felix Fröhlich, Jul 14 2019

CROSSREFS

Cf. A006512, A054735.

Sequence in context: A045158 A074328 A174185 * A170933 A297257 A296698

Adjacent sequences: A309149 A309150 A309151 * A309153 A309154 A309155

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 14 2019

STATUS

approved