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.

User: Patrick Capelle

Patrick Capelle's wiki page.

Patrick Capelle has authored 4 sequences.

A084195 Even numbers n such that the sum of the digits is prime, n/2 is prime and the sum of the digits of n/2 is also prime.

Original entry on oeis.org

14, 58, 94, 122, 166, 274, 278, 302, 346, 382, 386, 454, 458, 526, 562, 566, 634, 674, 706, 746, 818, 922, 926, 1114, 1154, 1198, 1202, 1282, 1286, 1466, 1514, 1594, 1642, 1646, 1774, 1822, 1954, 2038, 2078, 2102, 2182, 2186, 2218, 2258, 2326, 2362
Offset: 1

Views

Author

Patrick Capelle, Jun 20 2003

Keywords

Examples

			5+8=13 for n=58 and 2+9=11 for n/2=29=prime.
1+2+2=5 for n=122 and 6+1=7 for n/2=61=prime.
2+7+8=17 for n=278 and 1+3+9=13 for n/2=139=prime.

Crossrefs

Subsequence of A084194.

Programs

  • PARI
    isok(n) = {if (n % 2, return (0)); dn = digits(n); dh = digits(n/2); isprime(n/2) && isprime(sum(i=1, #dn, dn[i])) && isprime(sum(i=1, #dh, dh[i]));} \\ Michel Marcus, Aug 12 2013

Extensions

More terms from Michel Marcus, Aug 12 2013

A084194 Even numbers n such that the sum of the digits is prime and the sum of the digits of n/2 is also prime.

Original entry on oeis.org

14, 32, 50, 58, 76, 94, 98, 104, 122, 140, 148, 166, 184, 188, 212, 230, 238, 256, 274, 278, 292, 296, 302, 320, 328, 346, 364, 368, 382, 386, 410, 418, 436, 454, 458, 472, 476, 490, 494, 500, 508, 526, 544, 548, 562, 566, 580, 584
Offset: 1

Views

Author

Patrick Capelle, Jun 20 2003

Keywords

Comments

Sometimes n/2 is prime.

Examples

			3+2=5 for n=32 and 1+6=7 for n/2=16;
5+8=13 for n=58 and 2+9=11 for n/2=29;
2+1+2=5 for n=212 and 1+0+6=7 for n/2=106;
2+5+6=13 for n=256 and 1+2+8=11 for n/2=128.

Links

Crossrefs

Cf. A084201.

Programs

  • Maple
    filter:= proc(n)
  isprime(convert(convert(n,base,10),`+`)) and isprime(convert(convert(n/2,base,10),`+`))
end proc:
select(filter, [seq(i,i=2..1000,2)]); # Robert Israel, Sep 04 2019
  • PARI
    isok(n) = {if (n % 2, return (0)); dn = digits(n); dh = digits(n/2); isprime(sum(i=1, #dn, dn[i])) && isprime(sum(i=1, #dh, dh[i]));} \\ Michel Marcus, Aug 12 2013

Extensions

More terms from Michel Marcus, Aug 12 2013

A085626 Partial sums of A051935.

Original entry on oeis.org

2, 5, 11, 19, 29, 41, 59, 79, 101, 127, 157, 191, 227, 269, 313, 359, 409, 461, 521, 587, 659, 733, 809, 887, 967, 1049, 1151, 1259, 1373, 1489, 1607, 1733, 1861, 1993, 2129, 2267, 2411, 2557, 2707, 2861, 3019, 3181, 3347, 3517, 3691, 3877, 4073, 4271, 4481
Offset: 1

Views

Author

Patrick Capelle, Jul 10 2003

Keywords

Comments

Same as A070865 after first term. - David Wasserman, Jun 27 2005

Examples

			a(3) = 11 because it is the sum of the first 3 terms of A051935: 2+3+6 = 11.

Crossrefs

Cf. A051935, A070865.

A084201 Primes p such that the sum of the digits is prime and the sum of the digits of 2p is also prime.

Original entry on oeis.org

7, 29, 47, 61, 83, 137, 139, 151, 173, 191, 193, 227, 229, 263, 281, 283, 317, 337, 353, 373, 409, 461, 463, 557, 577, 599, 601, 641, 643, 733, 757, 797, 821, 823, 887, 911, 977, 1019, 1039, 1051, 1091, 1093, 1109, 1129, 1163, 1181, 1217, 1237, 1291
Offset: 1

Views

Author

Patrick Capelle, Jun 20 2003

Keywords

Comments

Note that 137 and 139 are twin primes.
A049084(A007953(a(n)))*A049084(A007953(2*a(n))) > 0. - Reinhard Zumkeller, Jun 26 2003

Examples

			2+9=11=prime for 29 and 5+8=13=prime for 58=2*29;
1+3+7=11=prime for 137 and 2+7+4=13=prime for 274=2*137;
1+3+9=13=prime for 139 and 2+7+8=17=prime for 278=2*139.

Links

Crossrefs

Subset of A084194/2.
Cf. A007953, A049084.

Programs

  • Maple
    filter:= proc(n)
  isprime(n) and isprime(convert(convert(n,base,10),`+`)) and isprime(convert(convert(2*n,base,10),`+`))
end proc:
select(filter, [seq(i,i=3..5000,2)]); # Robert Israel, Sep 04 2019
  • Mathematica
    Select[Prime[Range[300]],And@@PrimeQ[Total/@{IntegerDigits[#], IntegerDigits[2 #]}]&] (* Harvey P. Dale, Jun 26 2011 *)
Select[Prime[Range[500]],AllTrue[{Total[IntegerDigits[#]],Total[IntegerDigits[2#]]},PrimeQ]&] (* Harvey P. Dale, Jan 27 2025 *)

Extensions

More terms from Reinhard Zumkeller, Jun 26 2003
Offset changed to 1 by Robert Israel, Sep 04 2019

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

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