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.

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A118496 Reverse digits of largest Chen primes, append to sequence if result is larger Chen prime then previous one with reverse digits.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 101, 701, 941, 971, 991, 9001, 9011, 9221, 9521, 9941, 70001, 76001, 97001, 99401, 99431, 99571, 99989, 940001, 973001, 987101, 993401, 997811, 999431
Offset: 1

Views

Author

Jani Melik, May 05 2006

Keywords

Comments

Although Chen primes are a subset of primes, this sequence is not a subset of A098922. The first number that is not member of the later is 9011.

Crossrefs

Cf. A004087, A098922, A109611.

Programs

  • Maple
    # Check if number is Chen prime ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then return 'true' else return 'false' fi fi end: #Reverse digits obrni_stev:=proc(n) local i, tren, tren1, st, ans; ans:=[ ]: tren:=n: tren1:=0: for i while (tren>0) do st:=round(10*frac(tren/10)): ans:=[op(ans), st]: tren:=trunc(tren/10): od: for i from 0 to nops(ans)-1 do tren1:= tren1 + op(nops(ans)-i, ans)*10^(i): od: return tren1 end: ts_inv_prav_chen_pra:= proc(n) local i, tren, ans; tren:=0: ans:=[ ]: for i from 1 to n do if (ischenprime(i)='true' and ischenprime(obrni_stev(i))='true' and obrni_stev(i)>tren) then ans:=[op(ans),obrni_stev(i)]: tren:=obrni_stev(i): fi: od: return ans end: ts_inv_prav_chen_pra(200000);

A118497 Primes that are not Chen primes written backwards.

Original entry on oeis.org

34, 16, 37, 97, 79, 301, 151, 361, 371, 391, 322, 922, 142, 172, 772, 382, 313, 133, 943, 763, 373, 383, 793, 124, 334, 934, 754, 364, 325, 745, 395, 106, 706, 316, 916, 346, 166, 376, 196, 907, 727, 337, 937, 757, 377, 328, 358, 958, 388, 709, 929, 769, 799
Offset: 1

Views

Author

Jani Melik, May 05 2006

Keywords

Crossrefs

Cf. A004087, A102540, A109611.

Programs

  • Maple
    # Check if number is Chen prime ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then return 'true' else return 'false' fi fi end: #Reverse digits obrni_stev:=proc(n) local i, tren, tren1, st, ans; ans:=[ ]: tren:=n: tren1:=0: for i while (tren>0) do st:=round(10*frac(tren/10)): ans:=[op(ans), st]: tren:=trunc(tren/10): od: for i from 0 to nops(ans)-1 do tren1:= tren1 + op(nops(ans)-i, ans)*10^(i): od: return tren1 end: ts_inv_nonchen_pra:= proc(n) local i, trens, ans; trens:= [ ]; ans:=[ ]; for i from 1 to n do if (ischenprime( i ) = 'false') then ans:=[op(ans),obrni_stev(i)] fi: od: return ans end: ts_inv_nonchen_pra(2000);

A162707 Primes in A162706.

Original entry on oeis.org

5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 149, 163, 167, 173, 193
Offset: 1

Views

Author

Claudio Meller, Jul 11 2009

Keywords

Examples

			109 is in the list because it is the prime A000040(29) and can be written as 74+35=R(47)+R(53)= A004087(15)+A004087(16).

Extensions

Edited, entries checked by R. J. Mathar, Jul 13 2009
A-number in examples corrected - R. J. Mathar, Jul 23 2009

A162708 Numbers that are the sum of two reversed primes in more than one way.

Original entry on oeis.org

10, 14, 16, 18, 19, 20, 21, 22, 24, 27, 28, 30, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 66, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 81, 82, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109
Offset: 1

Views

Author

Claudio Meller, Jul 11 2009

Keywords

Comments

Subsequence of A162706. - R. J. Mathar, Jul 13 2009

Examples

			14 = R(7) + R(7) = R(3) + R(11).
28 = R(11) + R(71) = 11 + 17 = R(41) + R(41) = 14 + 14.
33 = 2 + 31 = R(2) + R(13) = 16 + 17 = R(61) + R(71).
36 = R(2) + R(43) = 2 + 34 = R(5) + R(13) = 5 + 31.

Programs

  • Maple
    read("transforms") ; A055642 := proc(n) max(1, ilog10(n)+1) ; end:
A004087 := proc(n) option remember; digrev(ithprime(n)) ; end:
isA162708 := proc(n) c := 0 ; for i from 1 do p := ithprime(i) ; if A055642(p) > A055642(n) then break; fi; for j from 1 to i do if A004087(i)+A004087(j) = n then c := c+1; fi; od: od: RETURN(c > 1); end:
for n from 1 to 200 do if isA162708(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Jul 13 2009

Extensions

Missing terms 14, 33, etc. inserted by R. J. Mathar, Jul 13 2009

A379938 Numbers k such that the k-th prime is a power of two reversed.

Original entry on oeis.org

1, 9, 18, 142, 575, 23652, 3633466, 10846595429, 802467018101, 2289255503212477
Offset: 1

Views

Author

Kalle Siukola, Jan 06 2025

Keywords

Examples

			The 9th prime is 23, 23 reversed is 32, and 32 = 2^5, so 9 is a term.

Crossrefs

Cf. A000040, A000079, A004087, A004094, A057708, A102385.

Programs

  • Python
    import sympy
for (k, p) in enumerate(sympy.primerange(10**8)):
    rev = int(str(p)[::-1])
    # is rev a power of two (or zero)?
    if rev & (rev - 1) == 0:
        print(k + 1, end=",")
print()

Formula

A000040(a(n)) = A102385(n).
a(n) = A000720(A102385(n)). - Michel Marcus, Jan 07 2025

Extensions

a(8)-a(10) from Amiram Eldar, Jan 07 2025
Previous Showing 31-35 of 35 results.

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