A303137 Numbers k such that concat(k, k-d(k)) and concat(k-d(k), k) are both prime, where d(k) is the number of divisors of k.

3, 29, 51, 53, 87, 177, 213, 291, 297, 357, 359, 399, 419, 427, 431, 471, 503, 521, 553, 561, 573, 597, 599, 659, 681, 687, 697, 719, 793, 871, 957, 987, 1019, 1163, 1243, 1261, 1501, 1539, 1633, 1843, 1957, 2037, 2213, 2273, 2339, 2441, 2511, 2639, 2741, 2753

Offset

1,1

Comments

Only squarefree numbers.

Like A284643 but using number of non-divisors.

Both k and k-d(k) must be odd to be eligeable for this sequence. This means that d(k) is even. Therefore, this sequence and A284643 cannot share common terms.

For 177, 573, 597, 687, 4809, 6223, 7693, 24069, etc. are prime k-d(k) and k+d(k) too.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Example

d(177) = 4 and concat(177,177-4) = 177173 and concat(177-4,177) = 173177 are both prime (like also 177 - 4 = 173 and 177 + 4 = 181).

Maple

select(n->isprime(n*10^(ilog10(n-tau(n))+1)+n-tau(n)) and isprime((n-tau(n))*10^(ilog10(n)+1)+n), [$3..2753]);

Prog

(PARI) isok(k) = my(sk = Str(k), sdk = Str(k-numdiv(k))); isprime(eval(concat(sk, sdk))) && isprime(eval(concat(sdk, sk))); \\ Michel Marcus, Apr 20 2018

Crossrefs

Cf. A000005, A049820, A284643.

Sequence in context: A087209 A165440 A072306 * A364076 A228613 A071150

Adjacent sequences: A303134 A303135 A303136 * A303138 A303139 A303140

Keyword

nonn,base,easy

Author

Paolo P. Lava, Apr 19 2018

Status

approved