A391947 Numbers k such that A003415(k) == A276085(k) (mod 2310) and A003415(k+1) == A276085(k+1) (mod 2310), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 27717, 41577, 69297, 131667, 159387, 235617, 242547, 270267, 277197, 332637, 346497, 519747, 540537, 595977, 713787, 803877, 852387, 928617, 1025637, 1178097, 1205817, 1212747, 1247397, 1288977, 1316697, 1344417, 1566177, 1621617, 1739427, 1760218, 1767147, 1850307, 1857237, 1884957, 1898817, 1933467, 1968117

Offset

1,2

Comments

Numbers k such that both k and k+1 are in A391864.

Question: Why is there such a strong bias towards terms ending with digit 7? There are only 33 exceptions among the first 386 terms: a(1)=1, a(31)=1760218, a(53)=2961418, a(64)=3695998, a(70)=4171858, etc.

Among the first 386 terms, there are only 16 terms that are not semiprimes: 1, 8290588, 8312140, 8466139, 9150314, 13394140, 14342788, 14816336, 15661510, 17613739, 20231740, 22150588, 24072508, 24433664, 29829028, 30669868, and none of these end in 7.

Links

Antti Karttunen, Table of n, a(n) for n = 1..386

Prog

(PARI) is_A391947(n) = (is_A391864(n) && is_A391864(1+n));

Crossrefs

Cf. A001221, A001222, A003415, A276085, A391864.

Sequence in context: A079321 A251235 A385362 * A023198 A230608 A204831

Adjacent sequences: A391944 A391945 A391946 * A391948 A391949 A391950

Keyword

nonn

Author

Antti Karttunen, Jan 17 2026

Status

approved