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A309152 Numbers that can be written as the sum of two primes whose difference is also prime. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 18 07:23 EDT 2021. Contains 345098 sequences. (Running on oeis4.)