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 1-4 of 4 results.

A385718 Primes p such that there exists prime q < p such that sigma(q+1) = sigma(p+2) = p + q.

Original entry on oeis.org

367, 457, 691, 341647, 909091, 1803421, 2640571, 3076903, 3413191, 5228611, 6152383, 6541477, 6545197, 6695503, 10161133, 10770313, 15319693, 31128511, 31687069, 39946483, 52764031, 58886803, 104494483, 207855001, 283882153, 307912921, 309201751, 529570609, 574061053
Offset: 1

Views

Author

S. I. Dimitrov, Jul 07 2025

Keywords

Comments

The primes q and p form a P(1, 2)-amicable pair. See Dimitrov link.

Examples

			(179, 367) is such a pair because sigma(179+1) = sigma(367+2) = 179 + 367.

Links

Crossrefs

Cf. A000040, A000203, A063990, A008333, A259180, A385586.

Extensions

More terms from Jinyuan Wang, Jul 07 2025

A385705 Primes p such that there exists prime q < p such that sigma(p+1)=sigma(q+1).

Original entry on oeis.org

37, 61, 109, 139, 157, 181, 193, 233, 269, 283, 347, 349, 353, 367, 373, 379, 487, 521, 541, 563, 571, 593, 613, 617, 619, 641, 643, 709, 727, 739, 797, 811, 823, 829, 853, 857, 877, 907, 983, 991, 1033, 1051, 1097, 1103, 1117, 1193, 1217, 1229, 1231, 1237
Offset: 1

Views

Author

S. I. Dimitrov, Jul 07 2025

Keywords

Examples

			(41, 61) is such a pair because sigma(41+1)=sigma(61+1) = 96.

Links

Crossrefs

Cf. A000203, A000040, A008333, A385586 (a subsequence).

Programs

  • Mathematica
    s={};Do[Do[If[DivisorSigma[1,Prime[m]+1]==DivisorSigma[1,Prime[n]+1],AppendTo[s,Prime[n]];Break[]],{m,n-1}],{n,203}];s (* James C. McMahon, Jul 08 2025 *)
  • PARI
    isok(p) = my(s=sigma(p+1)); forprime(q=1, p-1, if (sigma(q+1)==s, return(q))); \\ Michel Marcus, Jul 07 2025

A385739 Primes p such that there exists a prime q < p such that sigma(q-1) = sigma(p+1) = p + q.

Original entry on oeis.org

5563, 203431, 389923, 901423, 5495263, 7418863, 28128367, 188953969, 210627577, 392753209, 402877087, 505757683, 619418689, 2549153611, 2580356851, 3953660383, 5692944349, 6806206831, 6894059071, 7082199673, 10058113363, 11307503629, 12601725943, 12615171649
Offset: 1

Views

Author

S. I. Dimitrov, Jul 08 2025

Keywords

Comments

The primes q and p form a P(-1, 1)-amicable pair. Apparently (q-1, p+1) is an amicable pair A259180.

Examples

			(5021, 5563) is such a pair because sigma(5021-1) = sigma(5563+1) = 5021 + 5563.

Links

Crossrefs

Cf. A000040, A000203, A063990, A008333, A259180, A385586, A385718.

Extensions

a(5)-a(13) from Michel Marcus, Jul 08 2025
a(14)-a(24) from Giorgos Kalogeropoulos, Jul 14 2025

A385740 Primes p such that there exists a prime q < p such that sigma(p-1) = sigma(q-1) = p + q.

Original entry on oeis.org

1163, 7583, 17099, 48857, 65963, 172859, 5408423, 6804047, 19247087, 73162367, 77695043, 109775657, 109871933, 116464757, 160454717, 175031957, 175288493, 218543393, 268382183, 303220769, 379299989, 705800723, 823155779, 889218389, 967371143, 1100618483, 1242282407, 1701133163
Offset: 1

Views

Author

S. I. Dimitrov, Jul 08 2025

Keywords

Comments

The primes q and p form a P(-1, -1)-amicable pair. See Dimitrov link.

Examples

			(853, 1163) is such a pair because sigma(853-1) = sigma(1163-1) = 853 + 1163.

Links

Crossrefs

Cf. A000040, A000203, A063990, A008333, A259180, A385586, A385718, A385739.

Extensions

a(6)-a(25) from Michel Marcus, Jul 08 2025
a(26)-a(28) from Giorgos Kalogeropoulos, Jul 14 2025
Showing 1-4 of 4 results.

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