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A116222 Numbers n such that n+(n+1) is prime and sum of the prime factors of n and n+1 is also prime. 0
1, 2, 3, 9, 14, 20, 21, 30, 36, 41, 51, 68, 78, 83, 95, 99, 113, 131, 134, 135, 138, 153, 158, 209, 216, 249, 285, 299, 300, 303, 315, 320, 326, 350, 366, 375, 378, 413, 443, 453, 455, 468, 483, 488, 495, 498, 510, 543, 545, 615, 618, 645, 699, 713, 741, 771 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

83+84 = 167 is prime, 83 is prime, 84 = 2^2*3*7. 83+2+2+3+7 = 97 is prime, hence 83 is a term.

95+96 = 191 is prime. 95 = 5*19; 96 = 2^5*3. 5+19+2+2+2+2+2+3 = 37 is prime, hence 95 is a term.

PROG

(MAGMA) [1] cat [ n: n in [2..700] | IsPrime(2*n+1) and IsPrime(&+[ &+[ k[1]*k[2]: k in Factorization(h) ]: h in [n, n+1] ] ) ]; /* Klaus Brockhaus, Apr 17 2007 */

CROSSREFS

Sequence in context: A225792 A057293 A109662 * A338234 A048038 A113501

Adjacent sequences:  A116219 A116220 A116221 * A116223 A116224 A116225

KEYWORD

nonn

AUTHOR

J. M. Bergot, Apr 16 2007

EXTENSIONS

Edited, corrected and extended by Klaus Brockhaus, Apr 17 2007

STATUS

approved

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Last modified July 25 22:38 EDT 2021. Contains 346294 sequences. (Running on oeis4.)