cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A379963 Numbers k such that A276086(k)+1 is a perfect square (A000290), where A276086 is the primorial base exp-function.

Original entry on oeis.org

2, 8, 34, 36, 214, 248, 254, 2318, 2350, 2520, 2564, 2776, 5076, 30038, 30092, 30480, 32374, 510542, 510728, 510746, 512886, 515134, 540540, 540818, 542862, 542888, 1021442, 9699702, 9699722, 9699772, 9699788, 9702010, 9702256, 9729938, 9734358, 10210414, 10217558, 10240472, 10240724, 19401924, 19429870, 19912238
Offset: 1

Views

Author

Antti Karttunen, Jan 24 2025

Keywords

Examples

			A276086(34) = 63, +1 = 64 = 8^2, therefore 34 is included.
A276086(36) = 35, +1 = 36 = 6^2, therefore 36 is included.

Links

Crossrefs

Subsequence of A379962.
Cf. A000290, A002110, A276086.
Cf. also A379965 and A328849 (numbers k such that A276086(k) is a square).

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A379963(n) = issquare(1+A276086(n));

A379960 Numbers k such that A276086(k)-1 or A276086(k)+1 is a perfect power (A001597), where A276086 is the primorial base exp-function.

Original entry on oeis.org

1, 2, 4, 6, 7, 8, 13, 30, 34, 35, 36, 212, 214, 248, 254, 421, 2311, 2316, 2318, 2322, 2329, 2350, 2520, 2550, 2564, 2776, 4654, 5076, 9241, 30030, 30037, 30038, 30092, 30120, 30480, 32341, 32347, 32374, 34662, 60066, 510515, 510542, 510547, 510728, 510746, 512850, 512886, 515134, 540540, 540818, 542862, 542888, 1021442
Offset: 1

Views

Author

Antti Karttunen, Jan 22 2025

Keywords

Comments

Most terms seem to cluster after the primorials, A002110. (Compare also to the growth rate of A001597).

Examples

			See examples in A379961 and A379962.

Links

Crossrefs

Cf. A001597, A002110, A276086.
Union of A379961 and A379962.
Cf. also A379963.

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A379960(n) = { my(x=A276086(n)); (1==(x-1) || ispower(x+1) || ispower(x-1)); };

A379961 Numbers k such that A276086(k)-1 is a perfect power (A001597), where A276086 is the primorial base exp-function.

Original entry on oeis.org

1, 4, 6, 7, 13, 35, 212, 2311, 2316, 2322, 2329, 2550, 9241, 30030, 30037, 32341, 32347, 34662, 60066, 512850, 1023367, 223092876, 223092877, 223095199, 223097490, 223097491, 223122913, 446185741, 6469693260, 6479392984
Offset: 1

Views

Author

Antti Karttunen, Jan 24 2025

Keywords

Examples

			A276086(1) = 2, -1 = 1 = A001597(1), thus 1 is included.
A276086(2311) = 26, -1 = 25 = 5^2, thus 2311 is included.
A276086(1023367) = 328510, -1 = 328509 = 69^3, thus 1023367 is included.

Links

Crossrefs

Setwise difference A379960 \ A379962.
Cf. A001597, A276086.

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A379961(n) = { my(x=A276086(n)); (1==(x-1) || ispower(x-1)); };
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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