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A329590
Odd numbers k that cannot be expressed as k = p+q+r, with p prime and (q, r) a pair of twin primes.
0
1, 3, 5, 7, 9, 33, 57, 93, 99, 129, 141, 153, 177, 183, 195, 213, 225, 243, 255, 261, 267, 273, 297, 309, 327, 333, 351, 369, 393, 411, 423, 435, 453, 477, 489, 501, 513, 519, 525, 537, 561, 573, 591, 597, 603, 633, 645, 657, 663, 675, 687, 693, 705, 711, 723
OFFSET
1,2
EXAMPLE
33 can be expressed as the sum of three primes in 9 different ways:
33 = 11 + 11 + 11 = 13 + 13 + 7 = 17 + 11 + 5 = 17 + 13 + 3 = 19 + 7 + 7 = 19 + 11 + 3 = 23 + 5 + 5 = 23 + 7 + 3 = 29 + 2 + 2;
there is no pair of twin primes in the addends, so 33 is a term.
PROG
(PARI) for(n = 0, 500, m = 2*n+1; v = 0; forprime(i = 3, m-8, j = (m-i)/2; if(isprime(j-1) && isprime(j+1), v = 1)); if(v == 0, print1(m, ", ")))
(PARI) isok(k) = {if (! (k % 2), return (0)); forprime(p=3, k, if (isprime((k-p)\2-1) && isprime((k-p)\2+1), return(0)); ); return (1); } \\ Michel Marcus, Feb 16 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio Roldán, Feb 13 2020
STATUS
approved